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Engineers’ Guide to Rotating
Equipment
The Pocket Reference
Clifford Matthews
BSc, CEng, MBA, FIMechE
Professional Engineering Publishing Limited,
London and Bury St Edmunds, UK
First published 2002
This publication is copyright under the Berne Convention and the
International Copyright Convention. All rights reserved. Apart from any
fair dealing for the purpose of private study, research, criticism, or review,
as permitted under the Copyright Designs and Patents Act 1988, no part may
be reproduced, stored in a retrieval system, or transmitted in any form or by
any means, electronic, electrical, chemical, mechanical, photocopying,
recording or otherwise, without the prior permission of the copyright
owners. Unlicensed multiple copying of this publication is illegal. Inquiries
should be addressed to: The Publishing Editor, Professional Engineering
Publishing Limited, Northgate Avenue, Bury St Edmunds, Suffolk, IP32
6BW, UK.
ISBN 1 86058 344 X
© 2002 Clifford Matthews
A CIP catalogue record for this book is available from the British Library.
This book is intended to assist engineers and designers in understanding and
fulfilling their obligations and responsibilities. All interpretation contained
in this publication – concerning technical, regulatory, and design
information and data, unless specifically otherwise identified – carries no
authority. The information given here is not intended to be used for the
design, manufacture, repair, inspection, or certification of pressure
equipment, whether or not that equipment is subject to design codes and
statutory requirements. Engineers and designers dealing with pressure
equipment should not use the information in this book to demonstrate
compliance with any code, standard, or regulatory requirement. While great
care has been taken in the preparation of this publication, neither the author
nor the Publishers do warrant, guarantee, or make any representation
regarding the use of this publication in terms of correctness, accuracy,
reliability, currentness, comprehensiveness, or otherwise. Neither the
Publisher, Author, nor anyone, nor anybody who has been involved in the
creation, production, or delivery of this product shall be liable for any direct,
indirect, consequential, or incidental damages arising from its use.
Printed and bound in Great Britain by St Edmundsbury Press Limited,
Suffolk, UK
About the Author
Cliff has extensive experience as consulting/inspection engineer on
power/chemical plant projects worldwide: Europe, Asia, Middle East, USA,
Central and South America, and Africa. He has been an expert witness in a
wide variety of insurance investigations and technical disputes in power
plants, ships, paper mills, and glass plants concerning values of $40 m. Cliff
also performs factory inspections in all parts of the world including China,
USA, Western and Eastern Europe. He carries out site engineering in the
Caribbean – Jamaica, Bahamas, and the Cayman Islands.
Cliff is also the author of several books and training courses on pressure
equipment-related related subjects.
PREFACE
How to Use this Book
This book is intended to be an introductory guide to rotating equipment,
suitable for use as a ‘first port of call’ for information on the subject. It tries
to incorporate both technical and administrative aspects of rotating
equipment manufacture and use, introducing the basic principles of
balancing, vibration, noise, and inspection and testing of a wide range of
equipment. There is some well-established content and a few newer ideas. It
makes references to the most commonly used current and recent pressure
technical codes and standards, and attempts to simplify their complex
content into a form that is easier to understand. By necessity, therefore, the
content of this introductory book is not a substitute for the full text of
statutory instruments, regulations, and technical codes/standards. In all
cases, reference must be made to the latest edition of the relevant document
to obtain full, up-to-date information. Similarly, technical guidelines and
‘rules of thumb’ given in the book should be taken as just that – their only
purpose is to be useful.
This introductory guide to rotating equipment is divided into 14 main
chapters covering practical, theoretical, and legislative aspects of rotating
equipment technology. Content includes website and documentary
references for technical and regulatory information about rotating
equipment design and manufacture. Formal design-related information
appears in the referenced sources, while the websites provide a wide spread
of related information that can be used on a more informal basis. Most
information that you will need can be obtained from the websites, if you
know where to look.
Chapter 1 provides details of engineering units systems and mathematics,
essential to understanding the principles on which rotating equipment
performance is based. The basics of statics and deformable body mechanics
are given in Chapter 2, leading on to Chapter 3, which covers motion and
Engineers’ Guide to Rotating Equipmentviii
dynamics. The generic topics of balancing, vibration, and noise are
introduced in Chapter 4; these are common to virtually all types of rotating
equipment. Chapter 5 provides an outline of the various machine elements
that make up rotating machinery. Chapter 6, covering fluid mechanics, is a
necessarily theoretical chapter, providing formal explanations of essential
fluid mechanics principles used in the design of rotating fluid machinery.
Individual types of rotating equipment such as pumps, compressors,
turbines, and their associated power transmission equipment are outlined in
Chapters 7–10. Chapters 11 and 12 are practically orientated, looking at the
basic principles of mechanical design and material choice used in the design
of all types of rotating equipment. In common with other areas of
mechanical engineering, there have been rapid legislative developments
over the past few years; Chapter 13 provides detailed summaries of the
content and implications of The European Machinery Directives, and
mentions the proposed ‘Amending Directive 95/16/EC’ that may cause
further changes in the future.
Finally, the purpose of this introductory book is to provide a useful
pocket-size source of reference for engineers, technicians, and students with
activities in the rotating equipment business. If there is basic introductory
information about rotating equipment you need, I want you to be able to find
it here. If you have any observations about omissions (or errors) your
comments will be welcomed and used towards future editions of this book.
Please submit them to:
Ukdatabook2000@aol.com
If you have any informal technical comments you can submit them through
my website at: www.plant-inspection.org.uk
Clifford Matthews BSc, CEng, MBA, FIMechE
INTRODUCTION
The Role of Technical Standards
Technical standards play an important role in the design, manufacture, and
testing of rotating equipment components and machinery. In many cases,
rotating machines use a wide variety of types of technical standards:
complex, theoretically based topics for kinetic and dynamic design
complemented by more practical engineering-based standards for materials,
manufacture, non-destructive and pressure testing. Published standards also
have wide acceptance for vibration measurement and dynamic balancing of
rotating components and systems.
In common with other areas of mechanical engineering, rotating
equipment is increasingly subject to the regime of EU directives and their
corresponding harmonized standards. In particular, The Machinery
Directives are now well established, with wide-ranging influence on design,
manufacture, operation, and maintenance documentation. Harmonization is
not an instant process, however, and there are still many well-accepted
national standards (European and American) that are used as sound (and
proven) technical guidance.
Because of the complexity of rotating equipment, technical standards
relating to basic mechanical design (mechanics, tolerances, limit and fits,
surface finish, etc.) continue to be important. These standards form the
foundation of mechanical engineering and are based on sound experience,
gained over time.
One area of emerging technical standards is that of environmental
compliance. Most types of engines and prime movers come under the
classification of ‘rotating equipment’ and these machines are increasingly
subject to legislative limits on emissions and noise. Health and Safety
requirements are also growing, with new standards emerging covering
machine safety, integrity, and vibration limits.
Engineers’ Guide to Rotating Equipmentx
As in many engineering disciplines, technical standards relevant to
rotating equipment use several systems of units. Although the Système
International (SI) is favoured in Europe, the USA retains the use of the
USCS ‘imperial’ system, as do many other parts of the world. There are also
industry-specific preferences; the aerospace and offshore industries are still
biased, in many areas, towards imperial units-based technical standards.
These industries are big users of gas turbines, and other complex fluid
equipment.
In using the information in this book, it is important to refer to the latest
version of any published technical standard mentioned. New standards are
being issued rapidly as the European standards harmonization programme
progresses and there are often small and subtle changes in new versions of
previously well-established technical standards.
Contents
About the Author vi
Preface vii
Introduction ix
Chapter 1 Engineering Fundamentals 11.1 The Greek alphabet 11.2 Units systems 21.3 Conversions 41.4 Consistency of units 171.5 Foolproof conversions: using unity brackets 171.6 Imperial–metric conversions 191.7 Dimensional analysis 211.8 Essential mathematics 231.9 Useful references and standards 45
Chapter 2 Bending, Torsion, and Stress 472.1 Simple stress and strain 472.2 Simple elastic bending (flexure) 482.3 Slope and deflection of beams 512.4 Torsion 512.5 Combined bending and torsion 602.6 Stress concentration factors 61
Chapter 3 Motion and Dynamics 653.1 Making sense of dynamic equilibrium 653.2 Motion equations 653.3 Newton’s laws of motion 673.4 Simple harmonic motion 673.5 Understanding acceleration 683.6 Dynamic forces and loadings 693.7 Forces due to rotating masses 703.8 Forces due to reciprocating masses 70
Engineers’ Guide to Rotating Equipmentiv
Chapter 4 Rotating Machine Fundamentals: Vibration, Balancing, and Noise 71
4.1 Vibration: general model 714.2 Vibration formulae 724.3 Machine vibration 754.4 Dynamic balancing 784.5 Machinery noise 794.6 Useful references 81
Chapter 5 Machine Elements 835.1 Screw fasteners 835.2 Bearings 865.3 Mechanical power transmission – broad guidelines 905.4 Shaft couplings 915.5 Gears 995.6 Seals 1105.7 Cam mechanisms 1195.8 Belt drives 1215.9 Clutches 1235.10 Brakes 1285.11 Pulley mechanisms 1285.12 Useful references and standards 131
Chapter 6 Fluid Mechanics 1356.1 Basic properties 1356.2 Flow equations 1376.3 Flow regimes 1426.4 Boundary layers 1456.5 Isentropic flow 1466.6 Compressible one-dimensional flow 1476.7 Normal shock waves 1486.8 Axisymmetric flows 1516.9 Drag coefficients 151
Chapter 7 Centrifugal Pumps 1537.1 Symbols 1537.2 Centrifugal pump types 1537.3 Pump performance 1587.4 Pump characteristics 1627.5 Specifications and standards 1637.6 Test procedures and techniques 1647.7 Pump specific speed ns 1697.8 Pump balancing 1727.9 Balance calculations 1737.10 Pump components – clearances and fits 176
Chapter 8 Compressors and Turbocompressors 1818.1 Compressors 1818.2 Turbocompressors 188
Contents v
Chapter 9 Prime Movers 2039.1 Steam turbines 2039.2 Gas turbines – aeroderivatives 2239.3 Gas turbines – industrial 2349.4 Gearboxes and testing 2499.5 Reciprocating internal combustion engines 2559.6 Turbochargers 260
Chapter 10 Draught Plant 26310.1 Aeropropellers 26310.2 Draught fans 26710.3 ‘Fin-fan’ coolers 270
Chapter 11 Basic Mechanical Design 27511.1 Engineering abbreviations 27511.2 American terminology 27611.3 Preferred numbers and preferred sizes 27711.4 Datums and tolerances – principles 27811.5 Holes 28111.6 Screw threads 28211.7 Limits and fits 28311.8 Surface finish 28611.9 Reliability in design 28711.10 Improving design reliability: eight principles 28911.11 Design for reliability – a new approach 29211.12 Useful references and standards 294
Chapter 12 Materials of Construction 29512.1 Plain carbon steels – basic data 29512.2 Alloy steels – basic data 29512.3 Stainless steels – basic data 29612.4 Non-ferrous alloys – basic data 29912.5 Material traceability 299
Chapter 13 The Machinery Directives 30313.1 The Machinery Directive 98/37/EC – what is it? 30313.2 New Approach directives 30313.3 The scope of the Machinery Directive 30413.4 The CE mark – what is it? 30813.5 The technical file 31013.6 The declaration of conformity 31113.7 The role of technical standards 31513.8 The proposed ‘amending’ directive 95/16/EC 32613.9 Useful references and standards 328
Chapter 14 Organizations and Associations 329
Index 337
CHAPTER 1
Engineering Fundamentals
1.1 The Greek alphabetThe Greek alphabet is used extensively in Europe and the United States to
denote engineering quantities (see Table 1.1). Each letter can have various
meanings, depending on the context in which it is used.
Table 1.1 The Greek alphabet
Name Symbol
Capital Lower case
alpha Α α beta Β βgamma Γ γdelta ∆ δepsilon Ε εzeta Ζ ζeta Η η theta Θ θ iota Ι ι kappa Κ κlambda Λ λmu Μ µnu Ν νxi Ξ ξomicron Ο οpi Π π
Engineers’ Guide to Rotating Equipment2
rho Ρ ρ sigma Σ σtau Τ τupsilon Υ υphi Φ φchi Χ χpsi Ψ ψomega Ω ω
1.2 Units systemsIn the United States, the most commonly used system of units in the rotating
equipment industry is the United States Customary System (USCS). The
‘MKS system’ is a metric system still used in some European countries, but
gradually being superseded by the expanded Système International (SI)
system.
The USCS system
Countries outside the USA often refer to this as the ‘inch–pound’ system.
The base units are:
Length: foot (ft) = 12 inches (in)
Force: pound force or thrust (lbf)
Time: second (s)
Temperature: degrees Fahrenheit (°F)
The SI system
The strength of the SI system is its coherence. There are four mechanical
and two electrical base units from which all other quantities are derived.
The mechanical ones are:
Length: metre (m)
Mass: kilogram (kg)
Time: second (s)
Temperature: Kelvin (K) or, more commonly, degrees Celsius or
Centigrade (°C)
Other units are derived from these: for example the Newton (N) is defined
as N = kg m/s2.
Table 1.1 Cont.
Engineering Fundamentals 3
SI prefixes
As a rule, prefixes are generally applied to the basic SI unit. The exception
is weight, where the prefix is used with the unit gram (g), rather than the
basic SI unit kilogram (kg). Prefixes are not used for units of angular
measurement (degrees, radians), time (seconds) or temperature (°C or K).
Prefixes are generally chosen in such a way that the numerical value of a
unit lies between 0.1 and 1000 (see Table 1.2). For example
28 kN rather than 2.8 × 104 N
1.25 mm rather than 0.00125 m
9.3 kPa rather than 9300 Pa
Table 1.2 SI unit prefixes
Multiplication factor Prefix Symbol
1 000 000 000 000 000 000 000 000 = 1024 yotta Y
1 000 000 000 000 000 000 000 = 1021 zetta Z
1 000 000 000 000 000 000 = 1018 exa E
1 000 000 000 000 000 = 1015 peta P
1 000 000 000 000 = 1012 tera T
1 000 000 000 = 109 giga G
1 000 000 = 106 mega M
1 000 = 103 kilo k
100 = 102 hicto h
10 = 101 deka da
0.1 = 10–1 deci d
0.01 = 10–2 centi c
0.001 = 10–3 milli m
0.000 001 = 10–6 micro µ0.000 000 001 = 10–9 nano n
0.000 000 000 001 = 10–12 pico p
0.000 000 000 000 001 = 10–15 femto f
0.000 000 000 000 000 001 = 10–18 atto a
0.000 000 000 000 000 000 001 = 10–21 zepto z
0.000 000 000 000 000 000 000 001 = 10–24 yocto y
1.3 ConversionsUnits often need to be converted. The least confusing way to do this is by
expressing equality. For example, to convert 600 lb to kilograms (kg), using
1 kg = 2.205 lb
Add denominators as
Solve for x
Hence 600 lb = 272.1 kg
Setting out calculations in this way can help avoid confusion, particularly
when they involve large numbers and/or several sequential stages of
conversion.
Force or thrust
Force and thrust (see Table 1.3) are important quantities in determining the
stresses in a mechanical body. Both SI and imperial units are in common
use.
Table 1.3 Force (F) or thrust
Unit lbf gf kgf N
1 pound-thrust (lbf) 1 453.6 0.4536 4.448
1 gram-force (gf) 2.205×10–3 1 0.001 9.807×10–3
1 kilogram-force (kgf) 2.205 1000 1 9.807
1 Newton (N) 0.2248 102.0 0.1020 1
Note: Strictly, all the units in the table, except the Newton (N), represent weight
equivalents of mass and so depend on the ‘standard’ acceleration due to gravity (g). The
true SI unit of force is the Newton (N), which is equivalent to 1 kgm/s2.
Weight
The true weight of a body is a measure of the gravitational attraction of the
earth on it. Since this attraction is a force, the weight of a body is correctly
expressed in Newtons.
Engineers’ Guide to Rotating Equipment4
600 1272.1 kg
2.205x
×= =
1 kg 2.205 lb
600 lbx=
Engineering Fundamentals 5
Force (N) = mass (kg) × g(m/s2)
1 ton (US) = 2000 lb = 907.2 kg
1 tonne (metric) = 1000 kg = 2205 lb
Density
Density is defined as mass per unit volume. Table 1.4 shows the conversions
between units.
Table 1.4 Density (ρ)
Unit lb/in3 lb/ft3 kg/m3 g/cm3
1 lb per in3 1 1728 2.768 × 104 27.68
1 lb per ft3 5.787 × 10–4 1 16.02 1.602 × 10–2
1 kg per m3 3.613 × 10–5 6.243 × 10–2 1 0.001
1 g per cm3 3613 × 10–2 62.43 1000 1
Pressure
1 Pascal (Pa) = 1 N/m2
1 Pa = 1.450 38 × 10–4 lbf/in2
In practice, pressures in SI units are measured in MPa, bar, atmospheres,
Torr, or the height of a liquid column, depending on the application. See
Figs 1.1 and 1.2 and Table 1.5.
Fig. 1.1 Pressure equivalents
Engineers’ Guide to Rotating Equipment6
x 1000
x 6
.89
5. 1
0-3
x 1
45.0
3
x 1.0197
x 0.9807
x 10.0
x 0.1
x 0.09807
x 10.197
x 14.223
x 0.06895x 0.0703
PSI
BarsKg/cm2
N/mm2
(MPa)
x 14.503
‘KSI’
Fig. 1.2 Pressure conversions
Engin
eerin
g F
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Table 1.5 Pressure (p)
Unit lb/in2 (psi) lb/ft2 atm in H20 cm Hg N/m2 (Pa)
1 lb per in2 (psi) 1 144 6.805 × 10–2 27.68 5.171 6.895 × 103
1 lb per ft2 6.944 × 10–3 1 4.725 × 10–4 0.1922 3.591 × 10–2 47.88
1 atmosphere (atm) 14.70 2116 1 406.8 76 1.013 × 105
1 in of water at 39.2 °F (4 °C) 3.613 × 10–2 5.02 2.458 × 10–3 1 0.1868 249.1
1 cm of mercury at 32 °F (0 °C) 0.1934 27.85 1.316 × 10–2 5.353 1 1333
1 N per m2 (Pa) 1.450 × 10–4 2.089 × 10–2 9.869 × 10–6 4.015 × 10–3 7.501 × 10–4 1
Engineers’ Guide to Rotating Equipment8
So, for liquid columns
1 in H2O = 25.4 mm H2O = 249.089 Pa
1 in Hg = 13.59 in H2O = 3385.12 Pa = 33.85 mbar
1 mm Hg = 13.59 mm H2O = 133.3224 Pa = 1.333 224 mbar
1 mm H2O = 9.806 65 Pa
1 Torr = 133.3224 Pa
For conversion of liquid column pressures: 1 in = 25.4 mm
Temperature
The basic USCS unit of temperature is degrees Fahrenheit (°F). The SI unit
is Kelvin (K). The most commonly used unit is degrees Celsius (°C).
Absolute zero is defined as 0 K or –273.15 °C, the point at which a perfect
gas has zero volume. See Figs 1.3 and 1.4.
°C = 5/9 (°F – 32)
°F = 9/5 (°C) + 32
Heat and work
The basic unit for heat ‘energy’ is the Joule.
Specific heat ‘energy’ is measured in Joules per kilogram (J/kg) in SI
units and BTU/lb in USCS units.
1 J/kg = 0.429 923 × 10–3 BTU/lb
Fig. 1.3 Temperature
Engineering Fundamentals 9
Fig. 1.4 Temperature conversion
Table 1.6 shows common conversions.
Specific heat is measured in BTU/lb °F in USCS units [or in SI; Joules
per kilogram Kelvin (J/kg K)].
1 BTU/lb °F = 4186.798 J/kg K
1 J/kg K = 0.238 846 × 10–3 BTU/lb °F
1 kcal/kg K = 4186.8 J/kg K
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10
BTU ft-lb hp-h cal J kW-h
1 British thermal unit (BTU) 1 777.9 3.929 × 10–4 252 1055 2.93 × 10–4
1 foot-pound (ft-lb) 1.285 × 10–3 1 5.051 × 10–7 0.3239 1.356 3.766 × 10–7
1 horsepower-hour (hp-h) 2545 1.98 × 106 1 6.414 × 105 2.685 × 106 0.7457
1 calorie (cal) 3.968 × 10–3 3.087 1.559 × 10–6 1 4.187 1.163 × 10–6
1 Joule (J) 9.481 × 10–4 0.7376 3.725 × 10–7 0.2389 1 2.778 × 10–7
1 kilowatt hour (kW-h) 3413 2.655 × 106 1.341 8.601 × 105 3.6 × 106 1
Table 1.6 Heat
Engineering Fundamentals 11
Heat flowrate is also defined as power, with the USCS unit of BTU/h [or in
SI, in Watts (W)].
1 BTU/h = 0.07 cal/s = 0.293 W
1 W = 3.412 14 BTU/h = 0.238 846 cal/s
Power
BTU/h or horsepower (hp) are normally used in USCS or, in SI, kilowatts
(kW). See Table 1.7.
Flow
The basic unit of volume flowrate in SI is litre/s. In the USA it is US
gal/min.
1 US gallon = 4 quarts = 128 US fluid ounces = 231 in3
1 US gallon = 0.8 British imperial gallons = 3.788 33 litres
1 US gallon/minute = 6.314 01 × 10–5 m3/s = 0.2273 m3/h
1 m3/s = 1000 litre/s
1 litre/s = 2.12 ft3/min
Torque
The basic USCS unit of torque is the foot pound (ft.lbf) – in SI it is the
Newton metre (Nm). You may also see this referred to as ‘moment of force’
(see Fig. 1.5).
1 ft.lbf = 1.357 Nm
1 kgf.m = 9.81 Nm
Stress
In SI the basic unit of stress is the Pascal (Pa). One Pascal is an impractical
small unit so MPa is normally used (see Fig. 1.6). In the USCS system,
stress is measured in lb/in2 – the same unit used for pressure, although it is
a different physical quantity.
1 lb/in2 = 6895 Pa
1 MPa = 1 MN/m2 = 1 N/mm2
1 kgf/mm2 = 9.806 65 MPa
Engin
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12Table 1.7 Power (P)
BTU/h BTU/s ft-lb/s hp cal/s kW W
1 BTU/h 1 2.778 × 10–4 0.2161 3.929 × 10–4 7.000 × 10–2 2.930 × 10–4 0.2930
1 BTU/s 3600 1 777.9 1.414 252.0 1.055 1.055 × 10–3
1 ft–lb/s 4.628 1.286 × 10–3 1 1.818 × 10–3 0.3239 1.356 × 10–3 1.356
1 hp 2545 0.7069 550 1 178.2 0.7457 745.7
1 cal/s 14.29 0.3950 3.087 5.613 × 10–3 1 4.186 × 10–3 4.186
1 kW 3413 0.9481 737.6 1.341 238.9 1 1000
1 W 3.413 9.481 × 10–4 0.7376 1.341 × 10–3 0.2389 0.001 1
Engineering Fundamentals 13
Fig. 1.5 Torque
Fig. 1.6 Stress
Linear velocity (speed)
Linear velocity (see Table 1.8) is an important quantity in determining
kinetic forces in a component. The basic USCS unit for linear velocity is feet
per second (in SI it is m/s).
Table 1.8 Velocity (v)
Item ft/s km/h m/s mile/h cm/s
1 ft per s 1 1.097 0.3048 0.6818 30.48
1 km per h 0.9113 1 0.2778 0.6214 27.78
1 m per s 3.281 3.600 1 2.237 100
1 mile per h 1.467 1.609 0.4470 1 44.70
1 cm per s 3.281 × 10–2 3.600 × 10–2 0.0100 2.237 × 10–2 1
Acceleration
The basic unit of acceleration in SI is m/s2. The USCS unit is feet per second
squared (ft/s2).
1 kW1 hp
Length and area
Both SI and imperial units are in common use. Table 1.9 shows the
conversion.
Comparative lengths in USCS and SI units are:
1 ft = 0.3048 m
1 in = 25.4 mm
Small dimensions are measured in ‘micromeasurements’ (see Fig. 1.8).
1 ft/s2 = 0.3048 m/s2
1 m/s2 = 3.280 84 ft/s2
Standard gravity (g) is normally taken as 9.806 65 m/s2 (32.1740 ft/s2).
Angular velocity
The basic unit of angular velocity is radians per second (rad/s).
1 rad/s = 0.159 155 rev/s = 57.2958 degree/s
The radian is also the SI unit used for plane angles.
• A complete circle is 2π radians (see Fig. 1.7).
• A quarter-circle (90°) is π/2 or 1.57 radians.
• One degree = π/180 radians.
Engineers’ Guide to Rotating Equipment14
Fig. 1.7 Angular measure
Engin
eerin
g F
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Table 1.9 Area (A)
Unit sq in sq ft sq yd sq mile cm2 dm2 m2 a ha km2
1 square inch 1 – – – 6.452 0.064 52 – – – –
1 square foot 144 1 0.1111 – 929 9.29 0.0929 – – –
1 square yard 1296 9 1 – 8361 83.61 0.8361 – – –
1 square mile – – – 1 – – – – 259 2.59
1 cm2 0.155 – – – 1 0.01 – – – –
1 dm2 15.5 0.1076 0.011 96 – 100 1 0.01 – – –
1 m2 1550 10.76 1.196 – 10 000 100 1 0.01 – –
1 are (a) – 1076 119.6 – – 10 000 100 1 0.01 –
1 hectare (ha) – – – – – – 10 000 100 1 0.01
1 km2 – – – 0.386 1 – – – 10 000 100 1
Viscosity
Dynamic viscosity (µ) is measured in the SI system in Ns/m2 or Pascal
seconds (Pa s). In the USCS system it is lbf.s/ft2.
1 lbf.s/ft2 = 4.882 kgf.s/m2 = 4.882 Pa s
1 Pa s = 1 N s/m2 = 1 kg/m s
A common unit of dynamic viscosity is the centipoise (cP). See Table 1.10.
Table 1.10 Dynamic viscosity (µ)
Unit lbf-s/ft2 Centipoise Poise kgf/ms
1 lb (force)–s per ft2 1 4.788 × 104 4.788 × 102 4.882
1 Centipoise 2.089 × 10–5 1 10–2 1.020 × 10–4
1 Poise 2.089 × 10–3 100 1 1.020 × 10–2
1 N–s per m2 0.2048 9.807 × 103 98.07 1
Engineers’ Guide to Rotating Equipment16
Fig. 1.8 Making sense of microns
Engineering Fundamentals 17
• Kinematic viscosity (ν) is a function of dynamic viscosity.
• Kinematic viscosity = dynamic viscosity/density, i.e. ν = µ/ρ.
Units such as Saybolt Seconds Universal (SSU) and Stokes (St) are used.
The USCS unit is ft2/s.
1 m2/s = 10.7639 ft2/s = 5.580 01 × 106 in2/h
1 Stoke (St) = 100 centistokes (cSt) = 10–4 m2/s
1 St ≅ 0.002 26 (SSU) – 1.95/(SSU) for 32 < SSU < 100 s
1 St ≅ 0.002 20 (SSU) – 1.35/(SSU) for SSU > 100 s
1.4 Consistency of unitsWithin any system of units, the consistency of units forms a ‘quick check’
of the validity of equations. The units must match on both sides.
Example: (in USCS units)
To check kinematic viscosity (ν) =
Cancelling gives
OK, units match.
1.5 Foolproof conversions: using unity
bracketsWhen converting between units it is easy to make mistakes by dividing by
a conversion factor instead of multiplying, or vice versa. The best way to
avoid this is by using the technique of unity brackets.
A unity bracket is a term, consisting of a numerator and denominator in
different units, which has a value of unity.
For example
or
µ µ ρρ
= ×dynamic viscosity ( )1/
density ( )
= ×2 4
2 2
ft lbf.s ft
s ft lbf.s
= =2 4 2
2 2
ft s.ft ft
s ss .ft
2.205 lb
kg
kg
2.205 lb
are unity brackets, as are
or
or
As the value of the term inside the bracket is unity, it has no effect on any
term that it multiplies.
Example: Convert the density of titanium 6 Al 4 V; ρ = 0.16 lb/in3 to kg/m3
Step 1
State the initial value
Step 2
Apply the ‘weight’ unity bracket
Step 3
Apply the ‘dimension’ unity brackets (cubed)
Step 4
Expand and cancel*
ρ = 4428.02 kg/m3 : Answer
Engineers’ Guide to Rotating Equipment18
25.4 mm
in
in
25.4 mm
Atmosphere
101 325 Pa
ρ =3
0.16 lb
in
ρ = 3
0.16 lb kg
2.205 lbin
ρ =
3 3
3
0.16 lb kg in 1000 mm
2.205 lb 25.4 mm min
ρ = 0.16 lb3in
kg
2.205 lb
3in
( )3 325.4 mm
( )
3 31000 mm
3m
ρ =3
3 3
0.16 kg (1000)
2.205 (25.4) m
Engineering Fundamentals 19
* Take care to use the correct algebraic rules for the expansion, for example
(a.b)N = aN.bN
not
a.bN
And
expands to
Unity brackets can be used for all units conversions provided you follow the
rules for algebra correctly.
1.6 Imperial–metric conversionsConversions from metric to imperial units, and vice versa, often use
rounding to a prescribed number of significant figures. Table 1.11 shows a
conversion in common use.
Table 1.11 Imperial–metric conversions
Fraction (in) Decimal (in) Millimetre (mm)
1/64 0.01562 0.39687
1/32 0.03125 0.79375
3/64 0.04687 1.19062
1/16 0.06250 1.58750
5/64 0.07812 1.98437
3/32 0.09375 2.38125
7/64 0.10937 2.77812
1/8 0.12500 3.17500
9/64 0.14062 3.57187
5/32 0.15625 3.96875
11/64 0.17187 4.36562
3/16 0.18750 4.76250
13/64 0.20312 5.15937
7/32 0.21875 5.55625
15/64 0.23437 5.95312
31000 mm
m
3 3
3
(1000) .(mm)
(m)
1/4 0.25000 6.35000
17/64 0.26562 6.74687
9/32 0.28125 7.14375
19/64 0.29687 5.54062
15/16 0.31250 7.93750
21/64 0.32812 8.33437
11/32 0.34375 8.73125
23/64 0.35937 9.12812
3/8 0.37500 9.52500
25/64 0.39062 9.92187
13/32 0.40625 10.31875
27/64 0.42187 10.71562
7/16 0.43750 11.11250
29/64 0.45312 11.50937
15/32 0.46875 11.90625
31/64 0.48437 12.30312
1/2 0.50000 12.70000
33/64 0.51562 13.09687
17/32 0.53125 13.49375
35/64 0.54687 13.89062
9/16 0.56250 14.28750
37/64 0.57812 14.68437
19/32 0.59375 15.08125
39/64 0.60937 15.47812
5/8 0.62500 15.87500
41/64 0.64062 16.27187
21/32 0.65625 16.66875
43/64 0.67187 17.06562
11/16 0.68750 17.46250
45/64 0.70312 17.85937
23/32 0.71875 18.25625
47/64 0.73437 18.65312
3/4 0.75000 19.05000
49/64 0.76562 19.44687
25/32 0.78125 19.84375
51/64 0.79687 20.24062
Engineers’ Guide to Rotating Equipment20
Table 1.11 Cont.
Engineering Fundamentals 21
13/16 0.81250 20.63750
53/64 0.82812 21.03437
27/32 0.84375 21.43125
55/64 0.85937 21.82812
7/8 0.87500 22.22500
57/64 0.89062 22.62187
29/32 0.90625 23.01875
59/64 0.92187 23.41562
15/16 0.93750 23.81250
61/64 0.95312 24.20937
31/32 0.96875 24.60625
63/64 0.98437 25.00312
1 1.00000 25.40000
1.7 Dimensional analysis
Dimensional analysis (DA) – what is it?
Dimensional analysis is a technique based on the idea that one physical
quantity is related to others in a precise mathematical way. It is used in
rotating and hydraulic equipment design for:
• checking the validity of equations;
• finding the arrangement of variables in a formula;
• helping to tackle problems that do not possess a complete theoretical
solution, particularly those involving fluid mechanics.
Primary and secondary quantities
Primary quantities are quantities that are absolutely independent of each
other. They are
M Mass
L Length
T Time
For example: Velocity (v) is represented by length divided by time, and this
is shown by
[v] = : note the square brackets denoting ‘the dimension of’.
Table 1.12 shows the most commonly used quantities.
L
T
Table 1.11 Cont.
Table 1.12 Dimensional analysis quantities
Quantity Dimensions
Mass, m M
Length, l L
Time, t T
Area, a L2
Volume, V L3
First moment of area L3
Second moment of area L4
Velocity, v LT–1
Acceleration, a LT–2
Angular velocity, ω T–1
Angular acceleration, α T–2
Frequency, f T–1
Force, F MLT–2
Stress Pressure, S P ML–1T–2
Torque, T ML2T–2
Modulus of elasticity, E ML–1T–2
Work, W ML2T–2
Power, P ML2T–3
Density, ρ ML–3
Dynamic viscosity, µ ML–1T–1
Kinematic viscosity, ν L2T–1
Hence velocity is termed a secondary quantity because it can be expressed
in terms of primary quantities.
An example of deriving formulae using DA
To find the frequencies n of eddies behind a cylinder situated in a free
stream of pumped fluid, we can assume that n is related in some way to the
diameter d of the cylinder, the speed V of the fluid stream, the fluid density
ρ, and the kinematic viscosity ν of the fluid.
i.e.
n = φd, V, ρ, ν
Engineers’ Guide to Rotating Equipment22
Engineering Fundamentals 23
Introducing a numerical constant Y and some possible exponentials gives
n = Y d a, V b, ρ c, ν d
Y is a dimensionless constant so, in dimensional analysis terms, this
equation becomes, after substituting primary dimensions
T–1 = La(LT–1)b (ML–3)c (L2T–1)d
= La Lb T–b Mc L–3c L2d T–d
In order for the equation to balance
For M
c must = 0
For L
a + b – 3c + 2d = 0
For T
– b – d = – 1
Solving for a, b, c in terms of d gives
a = – 1 – d
b = 1 – d
Giving
n = d (– 1 – d) V (1 – d) ρ0 ν d
Rearranging gives
nd/V = (Vd/ν)X
Note how dimensional analysis can give the ‘form’ of the formula but not
the numerical value of the undetermined constant X which, in this case, is a
compound constant containing the original constant Y and the unknown
index d.
1.8 Essential mathematics
Basic algebra
am × an = am+n
am ÷ an = am–n
(am)n = amn
n√am = am/n
= a–n1na
ao = 1
(anbm)p = anpbmp
n√(ab) = n√a × n√b
Logarithms
If N = ax then loga N = x and N = alogaN
loga N =
log (ab) = log a + log b
log = log a – log b
log an = n log a
log n√a = log a
loga1 = 0
loge N = 2.3026 log10 N
Quadratic equations
If ax2 + bx + c = 0
x =
If b2 – 4ac > 0 the equation ax2 + bx + c = 0 yields two real and different
roots.
If b2 – 4ac = 0 the equation ax2 + bx + c = 0 yields coincident roots.
If b2 – 4ac < 0 the equation ax2 + bx + c = 0 has complex roots.
If α and β are the roots of the equation ax2 + bx + c = 0 then
sum of the roots = α + β = – product of the roots = αβ =
The equation whose roots are α and β is x2 – (α + β)x + αβ = 0.
Any quadratic function ax2 + bx + c can be expressed in the form
p (x + q)2 + r or r – p (x + q)2, where r, p, and q are all constants.
Engineers’ Guide to Rotating Equipment24
=n n
n
a a
b b
=n
n
n
a a
b b
√√√
log
logb
b
N
a
a
b
1
n
2
2
– ± ( – 4 )
a
b b ac√
b
a
c
a
Engineering Fundamentals 25
The function ax2 + bx + c will have a maximum value if a is negative and a
minimum value if a is positive.
If ax2 + bx + c = p(x + q)2 + r = 0 the minimum value of the function occurs
when (x + q) = 0 and its value is r.
If ax2 + bx + c = r – p(x + q)2 the maximum value of the function occurs
when (x + q) = 0 and its value is r.
Cubic equations
x3 + px2 + qx + r = 0
x = y – p gives y3 + 3ay + 2b = 0
where
3a = –q – p2, 2b = p3 – pq + r
On setting
S = [–b + (b2 + a3)1/2]1/3 and T = [–b – (b2 + a3)1/2]1/3
the three roots are
For real coefficients
all roots are real if b2 + a3 ≤ 0,
one root is real if b2 + a3 > 0.
At least two roots are equal if b2 + a3 = 0
Three roots are equal if a = 0 and b = 0.
For b2 + a3 < 0 there are alternative expressions
1
3
1
3
1
3
2
27
1
2
3
1
3
1 3 1(
2 2 3
1 3 1
2 2 3
= + –
= – + ) + ( – ) –
= – ( + ) – ( – ) – .
x S T p
x S T i S T p
x S T i S T p
√
√
1
2
3
2
3
1 1 2 cos
3 3
1 1 2 cos ( 2 )
3 3
1 1 2 cos ( 4 )
3 3
where and cos
x c p
x c p
x c p
bc a
c
θ
θ π
θ π
θ
= −
= + −
= + −
= − = −
Complex numbers
If x and y are real numbers and i = √–1 then the complex number z = x + iy
consists of real part x and the imaginary part iy.
z = x – iy is the conjugate of the complex number z = x + iy.
If x + iy = a + ib then x = a and y = b
(a + ib) + (c + id) = (a +c) = i(b + d)
(a + ib) – (c + id) = (a – c) + i(b – d)
(a + ib)(c + id) = (ac – bd) + i(ad + bc)
Every complex number may be written in polar form. Thus
x + iy = r(cos θ + i sin θ) = r∠θr is called the modulus of z and this may be written r = z
r = √(x2 + y2)
θ is called the argument and this may be written θ = arg z
If z1 = r(cos θ1 + i sin θ1) and z2 = r2(cos θ2 + i sin θ2)
z1z2 = r1r2[cos(θ1 + θ2) + i sin(θ1 + θ2)] = r1r2∠(θ1 + θ2)
Standard series
Binomial series
The number of terms becomes infinite when n is negative or fractional.
Engineers’ Guide to Rotating Equipment26
2 2 3 3
–1 2 2 2
2 3
1( ) 1 ... ( )
bx b x b xa bx b x a
a a a a
− = + + + + <
2 2 2 2
a ib ac bd bc adi
c id c d c d
+ + −= ++ + +
tany
xθ =
[ ]1 1 2 1 21 1
1 2
2 2 2
cos( ) sin( )( )
r iz r
z r r
θ θ θ θθ θ
− + += = ∠ −
1 2 2 3 3 2 2( 1) ( 1)( 2)( ) ... ( )
2! 3!
n n n n nn n n n na x a na x a x a x x a
− − −− − −+ = + + + + <
Engineering Fundamentals 27
Exponential series
Logarithmic series
Trigonometric series
Vector algebra
Vectors have direction and magnitude and satisfy the triangle rule for
addition. Quantities such as velocity, force, and straight-line dis-
placements may be represented by vectors. Three-dimensional vectors are
used to represent physical quantities in space, for example Ax, Ay, Az or
Ax i + Ay j + Az k.
2 3
2 3
( ln ) ( ln )1 ln ...
2! 3!
e 1 ...2! 3!
x
x
x a x aa x a
x xx
= + + + +
= + + + +
2 3
2 3
3 5
2 3 4
1 1ln = ( –1) – ( –1) + ( –1) – ... (0 < < 2)
2 3
–1 1 –1 1 –1 1ln = + + + ... >
2 3 2
–1 1 –1 1 –1ln = 2 . + + ... ( positive)
+1 3 +1 5 +1
ln (1+ ) = – + – + ...2 3 4
x x x x x
x x xx x
x x x
x x xx x
x x x
x x xx x
3 5 7
2 4 6
3 5 7 9 2
2
3 5 7
1 2
1 3 5 7 2
sin ...3! 5! 7!
cos 1 ...2! 4! 6!
2 17 62tan ...
3 15 315 2835 4
1 1 3 1 3 5sin ... ( 1)
2 3 2 4 5 2 4 6 7
1 1 1tan ... ( 1)
3 5 7
x x xx x
x x xx
x x x xx x x
x x xx x x
x x x x x x
π
−
−
= − + − +
= − + − +
= + + + + + <
⋅ ⋅ ⋅= + + + + <⋅ ⋅ ⋅
= − + − + ≤
Vector addition
The vector sum V of any number of vectors V1, V2, V3 where V1 = a1i + b1j
+ c1k, etc., is given by
V = V1 + V2 + V3 + ... = (a1 + a2 + a3 + ...)i
+(b1 + b2 + b3 + ...)j + (c1 + c2 + c3 + ...)k
Product of a vector V by a scalar quantity s
sV = (sa)i + (sb)j + (sc)k
(s1 + s2)V = s1V + s2V (V1 + V2)s = V1s + V2s
where sV has the same direction as V, and its magnitude is s times the
magnitude of V.
Scalar product of two vectors, V1
.V2
V1.V2 = |V1||V2|cosφ
where φ is the angle between V1 and V2.
Vector product of two vectors, V1 × V2
|V1 × V2| = |V1||V2|sinφwhere φ is the angle between V1 and V2.
Derivatives of vectors
If e(t) is a unit vector is perpendicular to e: that is e. = 0.
Gradient
The gradient (grad) of a scalar field φ (x, y, z) is
Engineers’ Guide to Rotating Equipment28
d d d( )
d d dt t t⋅ = ⋅ + ⋅B A
A B A B
d
d
e
t
d
d
e
t
d d d( )
d d d
d ( )
d
t t t
t
× = × + ×
= − ×
B AA B A B
B A
grad x y z
x y z
φ φ φ
φ φ φ
∂ ∂ ∂= ∇ = + + ∂ ∂ ∂ ∂ ∂ ∂= + +∂ ∂ ∂
i j k
i j k
Engineering Fundamentals 29
Divergence
The divergence (div) of a vector V = V(x, y, z) = Vx(x, y, z)i + Vy (x, y, z)j +
Vz (x, y, z)k
Curl
Curl (rotation) is
Differentiation
Rules for differentiation: y, u, and v are functions of x; a, b, c, and n are
constants.
div yx z
VV V
x y z
∂∂ ∂= ∇ ⋅ = + +∂ ∂ ∂
V V
curl y yz x z x
x y z
V VV V V V
x y z y z z x x y
V V V
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = ∇ × = = − + − + − ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
i j k
V V i j k
2
n n–1
n n 1
d d d(a b ) a b
d d d
d( ) d d
d d d
d 1 d d
d d d
d d d 1 n d( ) n ,
d d d d
u vu v
x x x
uv v uu v
x x x
u u u v
x v v x v x
u uu u
x x x u u x+
± = ±
= +
= − = = −
a
b
b b
a a
d d d1 , if 0
d dd
d d( ) ( )
d d
d( )d ( )
d
d( )d ( )
d
d( , )d d
d
d d d( , )d d ( , ) ( , )
d d d
x
x
v u
u v
u x x
u ux
uf u f u
x x
f t t f xx
f t t f xx
ff x t t t
x x
f v uf x t t t f x v f x u
x x x x
∂∂∂∂
= ≠
′=
=
= −
=
= + −
∫
∫
∫ ∫
∫ ∫
Higher derivatives
Second derivative =
Derivatives of exponentials and logarithms
Derivatives of trigonometric functions in radians
Engineers’ Guide to Rotating Equipment30
2
2
d d d( )
d d d
y yf x y
x x x
′′ ′′= = = 22 2
2 2
d d d( ) ( ) ( )
d d d
u uf u f u f u
x x x
′′ ′= +
n n 1
a a
a a
d(a b) na(a b)
d
de ae
d
d 1ln a , a 0
d
d da a ln a
d d
d 1 dlog log e
d d
x x
u u
x xx
x
x xx x
u
x x
uu
x u x
−+ = +
=
= >
=
=
2 2
2
d dsin cos , cos sin
d d
dtan sec 1 tan
d
dcot cosec x
d
x x x xx x
x x xx
xx
= = −
= = +
= −
2
2
2 1/ 2
d sinsec sec tan
d cos
d coscosec cosec cot
d sin
d d 1arcsin arccos
d d (1 )
xx x x
x x
xx x x
x x
x xx x x
= =
= − = −
= − =−
for angles in the first quadrant.
Engineering Fundamentals 31
Derivatives of hyperbolic functions
Partial derivatives
Let f(x, y) be a function of the two variables x and y. The partial derivative
of f with respect to x, keeping y constant, is
Similarly the partial derivative of f with respect to y, keeping x constant, is
Chain rule for partial derivatives
To change variables from (x, y) to (u, v) where u = u(x, y), v = v(x, y), both
x = x(u, v) and y = y(u, v) exist and f(x, y) = f [x(u, v), y(u, v)] = F(u, v).
Integration
f(x) F(x) = ∫f(x)dx
xa
x–1 ln |x|
ekx
ax
2 2
2 1/ 2 2 1/ 2
d dsinh cosh , cosh sinh
d d
d dtanh sech , cosh cosech
d d
d 1 d 1(arcsinh ) , (arccosh )
d ( 1) d ( 1)
x x x xx x
x x x xx x
x xx x x x
= =
= = −
±= =+ −
0
( , y) ( , y)limh
f f x h f x
x h→
∂ + −=∂
0
(x, ) (x, )limk
f f y k f y
y k→
∂ + −=∂
,
,
F x f y f F x f y f
u u x u y v v v v y
f u F v F f u F v F
x x u x v y y u y v
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂= + = +∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂= + = +∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
a 1
, a 1a 1
x +
≠ −+
ekx
k
a,a 0, a 1
ln a
x
> ≠
ln x x ln x – x
sin x – cos x
cos x sin x
tan x ln |sec x|
cot x ln |sin x|
sec x ln |sec x + tan x| = ln|tan ½(x + ½π)|
cosec x ln|tan ½ x|
sin2 x ½(x – ½ sin 2x)
cos2 x ½(x + ½ sin 2x)
sec2 x tan x
sinh x cosh x
cosh x sinh x
tanh x ln cosh x
sech x 2 arctan ex
cosech x ln |tanh ½x|
sech2x tanh x
Matrices
A matrix that has an array of (m × n) numbers arranged in m rows and n
columns is called an (m × n) matrix. It is denoted by
Engineers’ Guide to Rotating Equipment32
2 2
1
a x+1
arctan , a 0a a
x ≠
2 2
1
a x−
2 2 1/ 2
1
(a )x−
2 2 1/ 2
1
( a )x −
1 aln , a 0
2a a
1 aln , a 0
2a a
x
x
x
x
−− ≠ + − ≠ +
arcsin , a 0a
x ≠
2 2 1/ 2ln ( a )
arccosh , a 0a
x x
x
+ −
≠
Engineering Fundamentals 33
Square matrix
This is a matrix having the same number of rows and columns.
is a square matrix of order 3 × 3.
Diagonal matrix
This is a square matrix in which all the elements are zero, except those in
the leading diagonal.
is a diagonal matrix of order 3 × 3.
Unit matrix
This is a diagonal matrix with the elements in the leading diagonal all equal
to 1. All other elements are 0. The unit matrix is denoted by I.
Addition of matrices
Two matrices may be added provided that they are of the same order. This
is done by adding the corresponding elements in each matrix.
11 12 1
21 22 2
1 2
...
...
. . ... .
. . ... .
. . ... .
...
n
n
m m mn
a a a
a a a
a a a
11 12 13
21 22 23
31 32 33
a a a
a a a
a a a
11
22
33
0 0
0 0
0 0
a
a
a
1 0 0
0 1 0
0 0 1
I
=
13 13 13 13 11 12 11 12 11 11 12 12
23 23 23 23 21 22 21 22 21 21 22 22
a b a ba a b b a b a b
a b a ba a b b a b a b
++ + + = ++ +
I =
Subtraction of matrices
Subtraction is done in a similar way to addition except that the
corresponding elements are subtracted.
Scalar multiplication
A matrix may be multiplied by a number as follows
General matrix multiplication
Two matrices can be multiplied together provided the number of columns in
the first matrix is equal to the number of rows in the second matrix.
If matrix A is of order (p × q) and matrix B is of order (q × r) then if C =
AB, the order of C is (p × r).
Transposition of a matrix
When the rows of a matrix are interchanged with its columns the matrix is
said to be ‘transposed’. If the original matrix is denoted by A, its transpose
is denoted by A' or AT.
If A = then AT =
Adjoint of a matrix
If A = [aij] is any matrix and Aij is the cofactor of aij, the matrix [Aij]T is
called the adjoint of A. Thus
Engineers’ Guide to Rotating Equipment34
11 12 11 12 11 11 12 12
21 22 21 22 21 21 22 22
a a b b a b a b
a a b b a b a b
− − − = − −
11 12 11 12
21 22 21 22
a a ba bab
a a ba ba
=
11 12
1311 12
21 22
2321 22
31 32
11 11 12 21 13 31 11 12 12 22 13
21 11 22 21 23 31 21 12 22 22 23
b baa a
b baa a
b b
a b a b a b a b a b a b
a b a b a b a b a b a b
+ + + + = + + + +
1311 12
2321 22
aa a
aa a
11 21
12 22
13 23
a a
a a
a a
32
32
Engineering Fundamentals 35
A = adj A =
Singular matrix
A square matrix is singular if the determinant of its coefficients is zero.
The inverse of a matrix
If A is a non-singular matrix of order (n × n) then its inverse is denoted by
A–1 such that
AA–1 = I = A–1A
If A = A–1 =
Solutions of simultaneous linear equations
The set of linear equations
a11x1 + a12x2 + ... + a1nxn = b1
a21x1 + a22x2 + ... + a2nxn = b2
an1x1 + an2x2 + ... + annxn = bn
where the as and bs are known, may be represented by the single matrix
equation Ax = b, where A is the (n × n) matrix of coefficients, aij, and x and
b are (n × 1) column vectors. The solution to this matrix equation, if A is
11 12 1
21 22 2
1 2
...
...
. . .
. . .
. . .
...
n
n
n n nn
a a a
a a a
a a a
11 21 1
12 22 2
1 2
...
...
. . .
. . .
. . .
...
n
n
n n nn
A A A
A A A
A A A
1 adj ( )det ( )
cofactor of aij ij
− = ∆ =∆
=
AA A
A
11 12 1
21 22 2
1 2
...
...
. . ... .
. . ... .
. . ... .
...
n
n
n n nn
a a a
a a a
a a a
11 21 1
12 22 2
1 2
...
...
. . ... .1
. . ... .
. . ... .
...
n
n
n n nn
A A A
A A A
A A A
∆
… … … …
non-singular, may be written as x = A–1b which leads to a solution given by
Cramer’s rule
xi = det Di /det Ai = 1, 2, ..., n
where det Di is the determinant obtained from det A by replacing the
elements of aki of the ith column by the elements bk (k = 1, 2, …, n). Note
that this rule is obtained by using A–1 = (det A)–1 adj A and so again is of
practical use only when n ≤ 4.
If det A = 0 but det Di ≠ 0 for some i then the equations are inconsistent:
for example
x + y = 2, x + y = 3 has no solution.
Ordinary differential equations
A differential equation is a relation between a function and its derivatives.
The order of the highest derivative appearing is the order of the differential
equation. Equations involving only one independent variable are ‘ordinary’
differential equations, whereas those involving more than one are ‘partial’
differential equations.
If the equation involves no products of the function with its derivatives or
itself nor of derivatives with each other, then it is ‘linear’. Otherwise it is
‘non-linear’.
A linear differential equation of order n has the form
where Pi(i = 0, 1, ..., n), F may be functions of x or constants, and P0 ≠ 0.
First order differential equations
Form Type Method
Homogeneous Substitute
Separable
note that roots of q(y) = 0
are also solutions
1
0 1 11
d d d
d d d
n n
n nn n
y y yP P P P y F
x x x
−
−−+ + + + =
Engineers’ Guide to Rotating Equipment36
= d
d
y yf
x x
=d( ) ( )
d
yf x g y
x= +∫ ∫
d( )d
( )
yf x x C
g y
= yu
x
Engineering Fundamentals 37
Put
Exact
and solve these equations
for φφ(x, y) = constant is the
solution
Linear Multiply through by
Second order (linear) equations
These are of the form
When P0, P1, P2 are constants and f(x) = 0, the solution is found from the
roots of the auxiliary equation
P0m2 + P1m + P2 = 0
There are three other cases:
(i) Roots m = α and β are real and α ≠ βy(x) = Aeαx + Beβx
(ii) Double roots: α = βy(x) = (A + Bx) eax
(iii)Roots are complex: m = k ± il
y(x) = (A cos lx + B sin lx)ekx
Laplace transforms
If f(t) is defined for all t in 0 ≤ t < ∞, then
L[f(t)] = F(s) = ∫0∞
e–st f(t)dt
is called the Laplace transform of f(t). The two functions of f(t), F(s) are
known as a transform pair, and
∂ ∂∂ ∂
+ =
=
d( , ) ( , ) 0
d
and
yg x y f x y
x
f g
y x
∂φ ∂φ∂ ∂
= =andf gx y
+ =d( ) ( )
d
yf x y g x
x
=
= +
∫
∫
( ) exp( ( )d )
giving
( ) ( ) ( )d
x
x
p x f t t
p x y g s p s s C
2
0 1 22
d dP ( ) P ( ) P ( ) ( )
d d
y yx x x y F x
x x+ + =
f(t) = L–1[F(s)]
is called the inverse transform of F(s).
Function Transform
f(t), g(t) F(s), G(s)
c1f(t) + c2g(t) c1F(s) + c2G(s)
∫0tf(x)dx F(s)/s
(–t)nf(t)
eatf(t) F(s–a)
f(t–a)H(t–a) e–asF(s)
e–bt cos at
e–btcosh at
(πt)–1/2s
–1/2
s–(n + 1/2)
e–a√s
Basic trigonometry
Definitions (See Fig. 1.9)
sine: cosine:
Engineers’ Guide to Rotating Equipment38
d
d
n
n
F
s
d
d
n
n
f
t
− −
=− +∑ ( 1)
1
( ) (0 )n
n n r r
r
s F s s f
− >1e sin , 0bt
at aa + +2 2
1
( )s b a
++ +2 2( )
s b
s b a
− >1e sinh , 0bt
at aa + +2 2
1
( )s b a
++ +2 2( )
s b
s b a
π
−
⋅ ⋅ − √…
1/ 22, integer
1 3 5 (2 1)
n nt
nn
π− >
2
3 1/ 2
exp( / 4 ) ( 0)
2( )
a ta
t
siny
Ar
= cosx
Ar
=
Engineering Fundamentals 39
tangent: cotangent:
secant: cosecant:
Relations between trigonometric functions
sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A
cosec2 A = 1 + cot2 A
sin A = s cos A = c tan A = t
sin A s (1 – c2)1/2 t(1 + t2)–1/2
cos A (1 – s2)–1/2 c (1 + t2)–1/2
tan A s(1 – s2)–1/2 (1 – c2)1/2/c t
A is assumed to be in the first quadrant; signs of square roots must be chosen
appropriately in other quadrants.
tan y
Ax
=
secr
Ax
=
cotx
Ay
=
cosecr
Ay
=
Fig. 1.9 Basic trigonometry
Addition formulae
sin (A ± B) = sin A cos B ± cos A sin B
cos (A ± B) = cos A cos B sin A sin B
tan (A ± B) =
Sum and difference formulae
sin A + sin B = 2sin ½ (A + B) cos ½ (A – B)
sin A – sin B = 2cos ½ (A + B) sin ½ (A – B)
cos A + cos B = 2cos ½ (A + B) cos ½ (A – B)
cos A – cos B = 2sin ½ (A + B) sin ½ (B – A)
Product formulae
sin A sin B = ½cos (A – B) – cos (A + B)
cos A cos B = ½cos (A – B) + cos (A + B)
sin A cos B = ½sin (A – B) + sin (A + B)
Powers of trigonometric functions
sin2 A = ½ – ½ cos 2A
cos2 A = ½ + ½ cos 2A
sin3 A = ¾ sin A – ¼ sin 3A
cos3 A = ¾ cos A + ¼ cos 3A
Co-ordinate geometry
Straight-line
General equation ac + by + c = 0 m = gradient
c = intercept on the y-axis
Gradient equation y = mx + c
Intercept equation A = intercept on the x-axis
B = intercept on the y-axis
Perpendicular x cos α + y sin α = p p = length of perpendicular
equation from the origin to the line
α =angle that the
perpendicular makes
with the x-axis
Engineers’ Guide to Rotating Equipment40
tan tan
1 tan tan
A B
A B
±∓
1x y
A B+ =
±
Engineering Fundamentals 41
The distance between two points P(x1, y1) and Q(x2, y2) is given by
PQ = √[(x1 – x2)2 + (y1 – y2)
2]
The equation of the line joining two points (x1, y1) and (x2, y2) is given by
Circle
General equation x2 + y2 + 2gx + 2fy + c = 0
The centre has co-ordinates (–g, –f)
The radius is r = √(g2 + f 2 – c)
The equation of the tangent at (x1, y1) to the circle is
xx1 + yy1 + g(x + x1) + f(y + y1) + c = 0
The length of the tangent from (x1, y1) to the circle is
t2 = x12 + y1
2 + 2gx1 + 2fy1 + c
Parabola (see Fig. 1.10)
1 1
1 2 1 2
y y x x
y y x x
− −=− −
Fig. 1.10 Parabola
Engineers’ Guide to Rotating Equipment42
Eccentricity
With focus S(a, 0) the equation of a parabola is y2 = 4ax
The parametric form of the equation is x = at2, y = 2at
The equation of the tangent at (x1, y1) is yy1 = 2a(x + x1)
Ellipse (see Fig. 1.11)
Eccentricity
The equation of an ellipse is
The equation of the tangent at
The parametric form of the equation of an ellipse is x = a cos θ, y = b sin θ,
where θ is the eccentric angle
e 1SP
PD= =
1SP
ePD
= <
2 2
2 2 2
2 21 where (1 )
x yb a e
a b+ = = −
1 1
1 1 2 2( , ) is 1
xx yyx y
a b+ =
Fig. 1.11 Ellipse
Engineering Fundamentals 43
Hyperbola (see Fig. 1.12)
Eccentricity
The equation of a hyperbola is
The parametric form of the equation is x = a sec θ, y = b tan θ, where θ is
the eccentric angle
The equation of the tangent at
1SP
ePD
= >
2 2
2 2 2
2 21 where ( 1)
x yb a e
a b− = = −
1 1
1 1 2 2( , ) is 1
xx yyx y
a b− =
Fig. 1.12 Hyperbola
Sine wave (see Fig. 1.13)
y = a sin (bx + c)
y = a cos (bx + c´) = a sin (bx + c) (where c = c´ + π/2)
y = m sin bx + n cos bx = a sin (bx + c)
[where a = √(m2 + n2), c = tan–1(n/m)]
Helix (see Fig. 1.14)
A helix is a curve generated by a point moving on a cylinder with the
distance it transverses parallel to the axis of the cylinder being proportional
to the angle of rotation about the axis
x = a cos θ
y = a sin θ
z = kθ
(where a = radius of cylinder, 2πk = pitch)
Engineers’ Guide to Rotating Equipment44
Fig. 1.13 Sine wave
Engineering Fundamentals 45
1.9 Useful references and standardsFor links to The Reference Desk, a website containing over 6000 on-line
units conversions ‘calculators’, go to:
www.flinthills.com/~ramsdale/EngZone/refer.htm
Standards
1. ASTM/IEEE SI 10: 1997 Use of the SI system of units (replaces ASTM
E380 and IEEE 268).
Fig. 1.14 Helix
CHAPTER 2
Bending, Torsion, and Stress
2.1 Simple stress and strain
Hooke’s law:
= Young’s modulus E N/m2
2loadStress, units are N/m (see Fig. 2.1)
area
change in lengthStrain, a ratio, therefore, no units
original length
P
A
d
l
σ
ε
= =
= = =
lateral strain
longitudinal strain
d/d
l/l
δδ
=
Fig. 2.1 Stress and strain
stress constant
deformation=
Poisson’s ratio (v) =
(ratio, therefore, no units; see Fig. 2.2)
Engineers’ Guide to Rotating Equipment48
2.2 Simple elastic bending (flexure)The simple theory of elastic bending is
M = applied bending moment
I = second moment about the neutral axis
R = radius of curvature of neutral axis
E = Young’s modulus
σ = stress due to bending at distance y from neutral axis
= = M E
I y R
σ
Fig. 2.2 Poisson’s ratio
Fig. 2.3 Shear stress
Shear stress (τ) = : units: N/m2 (see Fig. 2.3)
Shear strain (γ) = angle of deformation under shear stress
Modulus of rigidity=
= constant G (units are N/m2)
shear load =
area
Q
A
shear stress =
shear strain
τγ
Bending, Torsion, and Stress 49
The second moment of area is defined, for any section, as
I = y2dA
I for common sections is calculated as follows in Fig. 2.4.
Fig. 2.4 I for common sections
Engineers’ Guide to Rotating Equipment50
Fig. 2.4 I for common sections (cont.)
Steelwork sections
Bending, Torsion, and Stress 51
Section modulus Z is defined as
Strain energy due to bending, U, is defined as
For uniform beams subject to constant bending moment this reduces to
2.3 Slope and deflection of beamsMany rotating equipment components (shafts, blades, bearings, etc.) can be
modelled as simple beams.
The relationships between load W, shear force SF, bending moment M,
slope, and deflection are:
Values for common beam configurations are shown in Fig. 2.5.
2.4 TorsionA torsional moment is a common occurrence in rotating equipment design
and can be treated in much the same way as bending, i.e. torsional moment
or torque (T) can be equated to a stress gradient multiplied by a second
moment of area. In this case the second moment (J) lies in the plane of stress
and is called the ‘polar second moment of area’ or ‘polar moment of inertia’
of the section. The stress in these conditions is shear stress, whose sign (i.e.
rotational tendency) reverses from one side of the centroid to the other.
IZ =
y
1 2
0
d
2
M sU
EI= ∫
2
2
Deflection = (or )
dSlope =
d
d
d
y
y
x
yM = EI
x
δ
3
3
4
4
d
d
d
d
yF = EI
x
yW = EI
x
2
2
M lU
EI=
Engineers’ Guide to Rotating Equipment52
Fig. 2.5 Slope and deflection of beams
Bending, Torsion, and Stress 53
For solid or hollow shafts of uniform cross-section, the torsion formula is
(see Figs 2.6 and 2.7)
T = torque applied (Nm)
J = polar second moment of area (m4)
τ = shear stress (N/m2)
R = radius (m)
G = modulus of rigidity (N/m2)
θ = angle of twist (rad)
l = length (m)
Fig. 2.6 Torsion
T G = =
J R l
τ θ
Engineers’ Guide to Rotating Equipment54
Fig. 2.7 Torsion formulae
Bending, Torsion, and Stress 55
For solid shafts
For hollow shafts
For thin-walled hollow shafts
J ≅ 2πr3t
where
r = mean radius of shaft wallt = wall thickness
Solid shaft with flange
Figure 2.8 shows the situation of a flanged shaft subjected to concentric
torsional loading. This is typically analysed as a system where the flange is
regarded as being rigidly held at its face and the flange thickness designed
so the stress at the junction of the shaft and flange is broadly equal to that at
the surface of the shaft. Hence, the design criteria become:
• area of possible fracture = πdt
• shear resistance = πdtτmax
• shear resistance moment (Tf) = πdtτmax × d/2
• for a balanced design, torque in flange (Tf) = torque in shaft (Tr)
hence using
and
Then
4
32
DJ =
π
( )4 4
32
D dJ =
π −
T
J R
τ=
4
32
dJ
π=
3
r max16
dT
π τ=
3
2
max max2 16
dd t
π πτ τ≅
Engineers’ Guide to Rotating Equipment56
Hence as a ‘rule of thumb’ for flange design; theoretical flange thickness
≥ d/8. In practice (and in flange design codes), the flange thickness is
increased above this minimum value to allow for the weakening effect of
flange bolt holes and the need for significant flange-to-flange bolting forces.
Strain energy (U) in torsion
In torsion, strain energy (U) is expressed as
Torsion of non-circular sections
If a section concentrically loaded in torsion is not of uniform circular shape,
the stress distribution is not a simple case. Since projections cannot carry
any stress at their tips, a stress gradient must exist between each tip and the
adjacent points of maximum stress. Stress is generally assumed to become a
maximum at approximately the greatest distance from the centre at which a
continuous circular annulus can be formed within the section. The stress
then varies uniformly between its maximum value and zero at the axis, and
between its maximum value and zero at the projection extremities. The
2 2
2 2
T l GJU
GJ l
θ= =
DIA
D
R
Fig. 2.8 Torsional loading of a flanged shaft
Bending, Torsion, and Stress 57
actual variation depends on the geometry of the projections. Torsion of a
plane rectangular section provides a good illustration.
Torsion of rectangular sections
Figure 2.9 shows a rectangular section of dimensions a × b. The maximum
shear stress (τmax) occurs at the middle of the long sides at point X, where the
largest continuous annulus can form. There is another smaller maximum at
the middle of the short sides at point Y. Stress at the corners and at the centre
is zero and the stress distribution over the sides is approximately parabolic,
as shown.
The relationship between the twisting moment T and the maximum shear
stress τmax at X is approximately
T = Kab2τmax
where constant K1
3 1.8b
a
≅+
Transmission of torque using keyed couplings
In a keyed coupling, the transmission of torque between concentric
components is achieved by means of transverse shear stress acting through
a longitudinal pin or key as shown in Fig. 2.10. If a single key is likely to
lead to unbalance in loading or weakness in the shaft section, two
diametrically opposed square keys of smaller size may be used. In certain
applications the key may be integral with the shaft, i.e. where stress intensity
Fig. 2.9 Stress distribution over a rectangular section
under torsion
Engineers’ Guide to Rotating Equipment58
is exceptionally high or the components need to slide relative to each other.
In this case the key is called a ‘spline’. The logical conclusion of this
concept is a splined shaft having a series of uniformly circumferentially
spaced splines engaging with a corresponding female socket, as shown in
Fig. 2.11. Some broad ‘rules of thumb’ in key sizing are:
1. The maximum key width w may be taken as d/4 where d is the shaft
diameter.
2. The effective key length (l) may be approximated to 3d/2 and the width
adjusted accordingly. With this proportion w≤d/4.
In either case the calculated key length should be increased to allow for the
rounded ends of the key (i.e. it will not provide full drive over its full
length).
Effective key
length (l)
Fig. 2.10 A square key end shape
Bending, Torsion, and Stress 59
Single-key, loose-flange couplings
Figure 2.12 shows typical outline design dimensions for a single-keyed
loose-flange coupling. Some typical design equations and crude rules of
thumb are:
• boss diameter (D) > 2d to allow for the keyway
• torque resistance of the key (Tk) when τk = allowable shear stress
in the key
• bolt shear resistance
where
n = number of bolts
δ = bolt diameter
• the pitch radius (R) of the bolts and the bolt diameter (δ) are found by
simple trial and error in the above equation. Normally, for a solid shaft, a
bolt diameter (δ) of δ = d/6 is a good starting point. Another typical
guideline calculation is
bolt diameter (δ) =
DIAMETER(d)
Fig. 2.11 ‘Keyed’ drives on shafts (a) A circular key
(b) A square key (c) A splined shaft
2
k8
ld τ≅
2
bolt( 1)
4
n πδ τ−≅
0.4238 mm
d
n+
√
Engineers’ Guide to Rotating Equipment60
2.5 Combined bending and torsionIn most practical rotating equipment applications, the effects of bending and
torsion do not exist in isolation, but are combined. The overall result is to
increase stress (and resulting fatigue) loadings, thereby increasing the
necessary factor of safety that has to be built in to the design if the
equipment is to perform satisfactorily.
For a shaft of diameter, d, in combined bending and torsion the following
equations are used:
Maximum resultant shear stress
τ =√where
p = tensile or compressive stress
q = shear stress acting on the same plane as p
Maximum safe shear stress
τmax =
DIA
D =
2d
Fig. 2.12 Single-keyed loose-flange coupling: typical
arrangement and dimensions
2
2
4
pq
+
E
3
16T
dπ
Bending, Torsion, and Stress 61
where
TE = √(M2 + T 2) termed the ‘equivalent torque’ resulting from bending and
moment, M, and torque, T.
Figure 2.13 shows a typical application of equivalent torque, TE, criterion for
a diesel engine crankshaft – a classic example of a combined bending
and torsion loading system. The figure also shows approximate design
dimensions in terms of the main journal diameter, D.
2.6 Stress concentration factorsThe effective stress in a component can be raised well above its expected
levels owing to the existence of geometrical features causing stress
concentrations under dynamic elastic conditions. Typical design stress
concentration factors are as shown in Fig. 2.14.
For the overhung crankshaft: Equivalent torque (TE) ≅ P√(L2+ R
2)
Fig. 2.13 Crankshaft: some torque design ‘rules of thumb’
Engineers’ Guide to Rotating Equipment62
Fig. 2.14 Stress concentration factors
Bending, Torsion, and Stress 63
Fig. 2.14 Stress concentration factors (cont.)
Engineers’ Guide to Rotating Equipment64
Fig. 2.14 Stress concentration factors (cont.)
CHAPTER 3
Motion and Dynamics
3.1 Making sense of dynamic equilibriumThe concept of dynamic equilibrium lies behind many types of engineering
analyses and design of rotating equipment. Some key definition points are:
• Formally, an object is in a state of equilibrium when the forces acting on
it are such as to leave it in its state of rest or uniform motion in a straight
line.
• In terms of dynamic equilibrium, this means that it is moving at constant
velocity with zero acceleration (or deceleration).
Figure 3.1 shows the difference between dynamic equilibrium and non-
equilibrium. The concept of dynamic equilibrium is used to design
individual components of rotating equipment.
3.2 Motion equations
Uniformly accelerated motion
Bodies under uniformally accelerated motion follow the general equations
v = u + at t = time (s)
s = ut + ½at2 a = acceleration (m/s2)
s = distance travelled (m)
u = initial velocity (m/s)
v2 = u2 + 2as v = final velocity (m/s)
2
u vs t
+=
Engineers’ Guide to Rotating Equipment66
Angular motion
t = time (s)
θ = angle moved (rad)
α = angular acceleration (rad/s2)
N = angular speed (rev/min)
ω1 = initial angular velocity (rad/s)
ω2 = final angular velocity (rad/s)
Fig. 3.1 Dynamic equilibrium and non-equilibrium
Dynamic equilibrium
Dynamic non-equilibrium
ω2 = ω1 + α
ω22 = ω1
2 + 2αs
θ = ω1t + ½α2
2
60
Nπω =
1 2
2t
ω ωθ −=
ωbωa
ωc
All parts of the
mechanism are
moving with constant
angular velocities
No parts of the
mechanism are
moving with constant
velocityAccelerating or
decelerating torque
αa=dωα/dt
Motion and Dynamics 67
General motion of a particle in a plane
v = ds/dt s = distance
a = dv/dt = d2s/dt2 t = time
v = adt v = velocity
s = vdt a = acceleration
3.3 Newton’s laws of motionFirst law A body will remain at rest or continue in uniform motion in a
straight line until acted upon by an external force.
Second law When an external force is applied to a body of constant mass
it produces an acceleration that is directly proportional to the
force, i.e. force (F) = mass (m) × acceleration (a).
Third law Every action produces an equal and opposite reaction.
Table 3.1 shows the comparisons between rotational and translational
motion.
Table 3.1 Comparisons: rotational and translational motion
Translation Rotation
Linear displacement from a datum x Angular displacement θLinear velocity v Angular velocity ωLinear acceleration a = dv/dt Angular acceleration α = dω/dt
Kinetic energy KE = mv2/2 Kinetic energy KE = Iω2
/2
Momentum mv Momentum Iω
Newton’s second law F = md2x/dt
2Newton’s second law M = d
2θ/dt2
3.4 Simple harmonic motionA particle moves with simple harmonic motion when it has constant angular
velocity, ω, and follows a displacement pattern
The projected displacement, velocity, and acceleration of a point P on the
x–y axes are a sinusoidal function of time, t. See Fig. 3.2.
0
2sin
60
Ntx x
π =
Engineers’ Guide to Rotating Equipment68
x0 = amplitude of the displacement
Angular velocity ω = 2πN/60, where N is in r/min
Periodic time T = 2π/ωVelocity, v, of point A on the x axis is
v = ds/dt = ωr sin ωt
Acceleration a = d2s/dt2 = dv/dt = –ω2r cos ωt
3.5 Understanding accelerationThe dangerous thing about acceleration in rotating components is that it
represents a rate of change of speed or velocity. When this rate of change is
high, it puts high stresses on the components, causing them to deform and
break. In practice, the components of engineering machines experience
acceleration many times the force of gravity, so they have to be designed to
resist the forces that result. These forces can be caused as a result of either
linear or angular accelerations, and there is a comparison between the two
as shown below:
Linear acceleration Angular acceleration
When analysing (or designing) any machine or mechanism, think about
linear accelerations first – they are always important.
Fig. 3.2 Simple harmonic motion
2m/s
v ua
t
−= 22 1 rad/st
ω ωα −=
Motion and Dynamics 69
3.6 Dynamic forces and loadingsThe design of rotating equipment is heavily influenced by the need to resist
dynamic loads in use.
Dynamic forces can be classified into three main groups:
• suddenly applied loads and simple impact forces;
• forces due to rotating masses;
• forces due to reciprocating masses.
In order to be able to chose design parameters, three factors have to be
considered:
• the energy to be absorbed;
• the elastic modulus, E, of the material of the impacted member;
• the elastic limit, Re, or the appropriate fatigue endurance limit, of the
material.
A basic ‘rule of thumb’ equation for impact situations is
where
σ = maximum generated stress
E = Young’s modulus of elasticity
X = Energy to be absorbed
V = Effective volume of the impacted member.
This equation uses the basic assumption that the impacted member is
infinitely rigidly supported and so absorbs all the energy, hence giving the
most severe stress conditions. In practical rotating equipment design factors
of approximately three to eight on static stress may be necessary to allow for
dynamic loadings.
For a situation where components are subjected to fatigue conditions, the
maximum permissible working stress must be adjusted according to the
desired life of the structure related to the frequency of the dynamic load
cycle. A long-life component (i.e. long life relative to number of cycles, say
107) requires an additional safety factor. As a guide, the factor should be
equal to at least 2.2 for stresses that fluctuate between zero and a maximum
in one direction, and at least 3.2 for stresses operating between equal
positive and negative stress maxima (e.g. tension and compression in a shaft
rotating under a bending moment).
If a rapid loading or impact cycle is repeated at relatively high uniform
frequency, then resonant or harmonic vibration may be set up in a structure,
causing severe overloading.
2 2EX
Vσ =
Engineers’ Guide to Rotating Equipment70
3.7 Forces due to rotating massesForces due to rotating masses are another significant factor in rotating
equipment design. The two main stresses generated are:
• stresses caused by centrifugal force;
• stresses resulting from inherently unbalanced rotating masses.
A basic formula is
Centrifugal force F =
where
W = weight of revolving body
v = velocity at radius k
g = acceleration due to gravity
n = r/min
The radius of gyration k is defined as the distance from the axis of swing to
the centre at which the whole rotating or oscillating mass may be regarded
as being concentrated, without involving any change in the moment of
inertia. (In this case, this is the true moment of inertia, and not the second
moment of area.)
If I is the moment of inertia, then
or
It is unusual for the centre of gyration (i.e. the point at which a mass may be
regarded as being concentrated) to coincide with the centre of gravity of the
mass, but they do coincide approximately if the radial depth of the mass is
small compared to the radius of gyration. In such a case, the radius of swing
of the centre of gravity may be used for calculation purposes instead of the
radius of gyration. A similar reasoning may be applied to calculations for the
rim of a wheel if the rim thickness is relatively small and the mass of the rim
is regarded as acting through the centroid of its area of cross-section.
3.8 Forces due to reciprocating massesFor simple analysis of rotating masses, it is usually assumed that the
reciprocation follows basic simple harmonic motion, see Fig. 3.2.
2 2 24
3600
Wv Wk n
gk g
π=
2WkI
g=
Igk
W
= √
CHAPTER 4
Rotating Machine Fundamentals: Vibration,
Balancing, and Noise
4.1 Vibration: general modelVibration is a subset of the subject of dynamics. It has particular relevance
to both structures and machinery in the way that they respond to applied
disturbances. The most common model of vibration is a concentrated
spring-mounted mass that is subject to a disturbing force and retarding
force, see Fig. 4.1.
The motion is represented graphically as shown by the projection of a
rotating vector x. Relevant quantities are
frequency (Hz) = √(k/m)/2πk = spring stiffness
m = mass
Fig. 4.1 Vibration: the general model
Engineers’ Guide to Rotating Equipment72
The ideal case represents simple harmonic motion with the waveform being
sinusoidal. Hence the motion follows the general pattern:
• vibration displacement (amplitude) = s
• vibration velocity = v = ds/dt
• vibration acceleration = a = dv/dt
4.2 Vibration formulaeThe four most common vibration cases are as shown below (see Fig. 4.2).
Free vibration: linear (Fig. 4.2 (a))
Free vibration: torsional (Fig. 4.2 (b))
Free damped vibration (Fig. 4.2 (c))
x = Ae–ξωnt sin (ωdt + ψ)
ωd = ωn√(1 – ζ 2)
cc = 2mωn
+ kx = F sin ωt
x = Ae–ξωnt sin (ωdt + ψ)
+ Xsin (ωt – φ)
( )n
n
0
sin
mx kx
x A t
k g
m
ω φ
ω∆
+ == −
= = √ √
( )t
n
t
n
0
sin
J k
A t
k
J
θ θθ ω φ
ω
+ == −
= √
0mx cx kx+ + =
0 1
2
1 2
21n 1n
(1 )
x x
x x
πζδζ
= = =√ −
mx cx+
Rotating Machine Fundamentals: Vibration, Balancing, and Noise 73
Forced vibration with damping (Fig. 4.2 (d))
X is maximum when r = √ (1 – 2ζ 2)
at resonance, r = 1
m mass
k spring constant
∆ static deflection
x displacement
A constant
ωn natural frequency
φ, ψ phase angle
kt torsional stiffness of shaft
J mass moment of inertia of flywheel
θ angular displacement
ζ = c/cc damping factor
c damping coefficient
cc critical damping coefficient
δ logarithmic decrement
ωd natural frequency of damped vibration
F maximum periodic force
X0 equivalent static deflection = F/k
( ) ( )
( ) ( )
2 22
2 320
2
/
1 2
1
1 2
2tan
1
[ ]
[ ]
F kX
r r
XD
Xr r
r
r
ζ
ζ
ζφ
=− +
= =− +
=−
√
√
max
2
0
1
2 (1 )
X
X ζ ζ=
√ −
21tan (1 2 )φ ζ
ζ= √ −
0
re
n2
F XX
cω ζ= =
Engineers’ Guide to Rotating Equipment74
Xmax peak amplitude
Xre amplitude at resonance
r = ω/ωn, frequency ratio
D dynamic magnifier
Fig. 4.2 Vibration modes
Rotating Machine Fundamentals: Vibration, Balancing, and Noise 75
4.3 Machine vibrationThere are two main types of vibration relevant to rotating machines:
• bearing housing vibration. This is assumed to be sinusoidal. It normally
uses the velocity (Vrms) parameter.
• shaft vibration. This is generally not sinusoidal. It normally uses dis-
placement (s) as the measured parameter.
Bearing housing vibration
Relevant points are:
• only vibration at the ‘surface’ is measured;
• torsional vibration is excluded;
• Vrms is normally measured across the frequency range and then distilled
down to a single value, i.e. Vrms = √[½Σ(amplitudes × angular frequences)].
Acceptance levels
Technical standards and manufacturers’ practices differ in their acceptance
levels. General ‘rule of thumb’ acceptance levels are shown in Tables 4.1
and 4.2, and Fig. 4.3.
Table 4.1 Balance quality grades (ISO 1940)
Balance eω* Rotor types – general examples
quality (mm/s)
grade G
G 4000 4000 Crankshaft drives of rigidly mounted, slow marine diesel
engines with uneven number of cylinders
G 1600 1600 Crankshaft drives of rigidly mounted, large, two-cycle
engines
G 630 630 Crankshaft drives of rigidly mounted, large, four-cycle
engines
Crankshaft drives of elastically mounted marine diesel
engines
G 250 250 Crankshaft drives of rigidly mounted, fast, four-cylinder
diesel engines
G 100 100 Crankshaft drives of fast diesel engines with six or more
cylinders
Complete engines (gasoline or diesel) for cars, trucks,
and locomotives
G 40 40 Car wheels, wheel rims, wheel sets, drive shafts
Crankshaft drives of elastically mounted, fast, four-cycle
engines (gasoline or diesel) with six or more cylinders
Engineers’ Guide to Rotating Equipment76
Crankshaft drives for engines of cars, trucks, and
locomotives
G 16 16 Drive shafts (propeller shafts, cardan shafts) with special
requirements
Parts of crushing machinery
Parts of agricultural machinery
Individual components of engines (petrol or diesel) for
cars, trucks, and locomotives
Crankshaft drives of engines with six or more cylinders
under special requirements
G 6.3 6.3 Parts of process plant machines
Marine main turbine gears
Centrifuge drums
Fans
Assembled aircraft gas turbine rotors
Flywheels
Pump impellers
Machine-tool and general machinery parts
Normal electrical armatures
Individual components of engines under special
requirements
G 2.5 2.5 Gas and steam turbines, including marine main turbines.
Rigid turbogenerator rotors
Rotors
Turbocompressors
Machine-tool drives
Medium and large electrical armatures with special
requirements
Small electrical armatures
Turbine-driven pumps
G 1 1 Tape recorder and phonograph (gramophone) drives
Grinding-machine drives
Small electrical armatures with special requirements
G 0.4 0.4 Spindles, disks, and armatures of precision grinders
Gyroscopes
*ω = 2π x N/60 ∝ n/10, if n is measured in r/min and ω in rad/s. e is the
eccentricity of the centre of gravity.
Table 4.1 Cont.
Balance grade Type of rotor (general examples)
G 1 Grinding machines, tape-recording equipment
G 2.5 Turbines, compressors, electric armatures
G 6.3 Pump impellers, fans, gears, machine tools
G 16 Cardan shafts, agriculture machinery
G 40 Car wheels, engine crankshafts
G 100 Complete engines for cars and trucks
Rotating Machine Fundamentals: Vibration, Balancing, and Noise 77
Table 4.2 General ‘rules of thumb’ acceptance levels
Machine Vrms (mm/s)
Precision components and machines – gas turbines, etc. 1.12
Helical and epicyclic gearboxes 1.8
Spur-gearboxes, turbines 2.8
General service pumps 4.5
Long-shaft pumps 4.5–7.1
Diesel engines 7.1
Reciprocating large machines 7.1–11.2
Fig. 4.3 Vibration balance grades ISO 10816-1
Typical balance grades; from ISO 1940–1
Engineers’ Guide to Rotating Equipment78
4.4 Dynamic balancingAlmost all rotating machines (pumps, shafts, turbines, gearsets, generators,
etc.) are subject to dynamic balancing during manufacture. The objective is
to maintain the operating vibration of the machine within manageable limits.
Dynamic balancing normally comprises two measurement/correction
planes and involves the calculation of vector quantities. The component is
mounted in a balancing rig which rotates it at near its operating speed, and
both senses and records out-of-balance forces and phase angle in two planes.
Balance weights are then added (or removed) to bring the imbalance forces
to an acceptable level (see Fig. 4.4). Figure 4.5 shows how to interpret the
corresponding vibration readings.
Fig. 4.4 Dynamic balancing
Rotating Machine Fundamentals: Vibration, Balancing, and Noise 79
Balancing standards
The international standards ISO 1940-1 (1984) Balance and quality
requirements of rigid rotors and ISO 10816-1 are frequently used. Finer
balance grades are used for precision assemblies such as instruments and
gyroscopes. The nearest American equivalent is ANSI/ASA standard ANSI
S2.42 (1997) Balancing of flexible rotors. This also classifies rotors into
groups in accordance with various balance ‘quality’ grades.
4.5 Machinery noise
Principles
Noise is most easily thought of as airborne pressure pulses set up by a
vibrating surface source. It is measured by an instrument that detects these
pressure changes in the air and then relates this measured sound pressure
to an accepted zero level. Because a machine produces a mixture of
frequencies (termed ‘broad-band’ noise), there is no single noise
measurement that will fully describe a noise emission. In practice, two
methods used are:
Fig. 4.5 How to interpret vibration readings
Engineers’ Guide to Rotating Equipment80
• The ‘overall noise’ level. This is often used as a colloquial term for what
is properly described as the A-weighted sound pressure level. It
incorporates multiple frequencies, and weights them according to a
formula that results in the best approximation of the loudness of the noise.
This is displayed as a single instrument reading expressed as decibels
dB(A).
• Frequency band sound pressure level. This involves measuring the sound
pressure level in a number of frequency bands. These are arranged in
either octave or one-third octave bands in terms of their mid-band
frequency. The range of frequencies of interest in measuring machinery
noise is from about 30 Hz to 10 000 Hz. Note that frequency band sound
pressure levels are also expressed in decibels (dB).
The decibel scale itself is a logarithmic scale – a sound pressure level in dB
being defined as
dB = 10 log10 (p1/p0)2
where
p1 = measured sound pressure
p0 = a reference zero pressure level
Noise tests on rotating machines are carried out by defining a ‘reference
surface’ and then positioning microphones at locations 3 ft (0.91 m) from it
(see Fig. 4.6).
Typical levels
Approximate ‘rule of thumb’ noise levels are given in Table 4.3.
Table 4.3 Typical noise levels
Machine/environment dB(A)
A whisper 20
Office noise 50
Noisy factory 90
Large diesel engine 97
Turbocompressor/gas turbine 98
A normal ‘specification’ level is 90–95 dB(A) at 1 m from operating
equipment. Noisier equipment needs an acoustic enclosure. Humans can
continue to hear increasing sound levels up to about 120 dB. Levels above
this cause serious discomfort and long-term damage.
Rotating Machine Fundamentals: Vibration, Balancing, and Noise 81
4.6 Useful references
Standards: balancing
1. API publication 684: (1992) First edition, A tutorial on the API approach
to rotor dynamics and balancing.
2. SAE ARP 5323: (1988) Balancing machines for gas turbine rotors.
Standards: vibration
Table 4.4 shows the status of some relevant technical standards dealing with
vibration.
Fig. 4.6 Noise tests on rotating machines
Engineers’ Guide to Rotating Equipment82
Table 4.4 Technical standards – vibration
See also Table 13.11 showing harmonized standards relevant to the
machinery directive.
Standards: noise
1. ANSI/ASA S12.16: (1997) American National Standard Guidelines for
the specification of noise from new machinery.
2. ANSI/ASA S12.3: (1996) American National Standard Statistical
methods for determining and verifying stated noise emission values of
machinery and equipment.
3. ISO 10494: (1993) Gas turbine and gas turbine sets – measurement of
emitted airborne noise – engineering (survey method).
Standard Title Status
BS 4675-2: 1978,
ISO 2954-1975
Mechanical vibration in rotating
machinery. Requirements for
instruments for measuring vibration
severity.
Current
CP 2012-1: 1974 Code of practice for foundations for
machinery. Foundations for
reciprocating machines.
Current
BS EN 1032: 1996 Mechanical vibration. Testing of
mobile machinery in order to
determine the whole-body vibration
emission value. General.
Current
Work in hand
BS EN 12786:
1999
Safety of machinery. Guidance for the
drafting of vibration clauses of safety
standards.
Current
00/710581 DC ISO/DIS 14839-1 Mechanical
vibration of rotating machinery
equipped with active magnetic
bearings. Part 1. Vocabulary.
Current
Draft for
public
comment
BS 4675: Part 1:
1976, ISO 2372-
1974
Mechanical vibration in rotating
machinery. Basis for specifying
evaluation standards for rotating
machines with operating speeds from
10 to 200 rev/s.
Withdrawn
Superseded
CHAPTER 5
Machine Elements
‘Machine elements’ is the term given to the set of basic mechanical
components that are used as building blocks to make up a rotating
equipment product or system. There are many hundreds of these; the most
common ones are shown, subdivided into their common groupings, in Fig.
5.1. The established reference source for the design of machine elements is:
• Shigley, J.E. and Mischke, C.R. (1996) Standard handbook of machine
design, Second edition, McGraw Hill, ISBN 0-07-056958-4.
5.1 Screw fastenersThe ISO metric and, in the USA, the unified inch and ISO inch are
commonly used in rotating equipment designs. They are covered by
different technical standards, depending on their size, material, and
application.
Dimensions: ISO metric fasteners (ISO 4759)
Table 5.1 and Fig. 5.2 show typical dimensions (all in mm) for metric
fasteners covered by ISO 4759.
Table 5.1 ISO metric fastener dimensions (mm)
Size Pitch Width A/F (F) Head height (H) Nut thickness (m)
max min max min max min
M5 0.8 8.00 7.85 3.650 3.350 4.00 3.7
M8 1.25 13.00 12.73 5.650 5.350 6.50 6.14
M10 1.5 17.00 16.73 7.180 6.820 8.00 7.64
M12 1.75 19.00 18.67 8.180 7.820 10.00 9.64
M20 2.5 30.00 29.67 13.215 12.785 16.00 15.57
Engin
eers
’G
uid
e to
Rota
ting E
quip
ment
84
Locating
Threaded fasteners
Nuts and bolts
Set screws
Studs
Grub screws
Expanding bolts
Keys
Flat
Taper
Woodruff
Profiled
Pins
Split
Taper
Splines
Retaining rings
Clamps
Clips
Circlips
Spring
Shoulders and grooves
Drives and mechanisms
Shafts
Parallel
Taper
Concentric
Mechanisms
Crank and sliding
Ratchet and pawl
Geneva
Scotch-yolk
Carden joint
Cams
Constant velocity
Uniform acceleration
Simple harmonic
Motion (s.h.m.)
Clutches
Dog
Cone
Disc
Spring
Magnetic
Fluid coupling
Brakes
Disk
Drum
Couplings
Rigid
Flexible
Spring
Membrane
Cordon
Claw
Energy transmission
Gear trains
Spur
Helical
Bevel
Worm and wheel
Epicyclic
Belt drives
Flat
Vee
Wedge
Synchronous
Chain drives
Roller
Conveyor
Leaf
Pulleys
Simple
Differential
Springs
Tension
Compression
Rotary bearings
Rolling
Ball
Roller (parallel)
Roller (tapered)
Needle
Self-aligning
Sliding
Axial
Radial
Bush
Hydrodynamic
Hydrostatic
Self-lubricating
Slideways
Dynamic sealing
Rotating shaft seals
Face
Interstitial
Axial radial
Bush
Labyrinth
Lip ring
Split ring
Reciprocating shaft seals
Piston rings
Packing rings
Fig
. 5.1
Mach
ine e
lem
en
ts
Machine Elements 85
Unified inch screw threads (ASME B1.1)
Fasteners are defined by their combination of diameter–pitch relationship
and tolerance class. Table 5.2 shows the system of unified inch thread
designation (see also Table 5.3 for UNC/UNRC thread dimensions).
Table 5.2 Unified inch thread relationships
Diameter–pitch relationship Tolerance class
UNC and UNRC: Coarse A represents external threads
UNF and UNRF: Fine B represents internal threads
UN and UNR: Constant pitch Class 1: Loose tolerances for easy
assembly
UNEF and UNREF: Extra fine Class 2: Normal tolerances for production
items
Class 3: Close tolerances for accurate
location application
Table 5.3 Typical* UNC/UNRC thread dimensions
Nominal size (in) Basic major Threads per Basic minor
diameter D (in) inch (in) diameter K (in)
1/8 0.125 40 0.0979
1/4 0.25 20 0.1959
1/2 0.50 13 0.4167
1 1.00 8 0.8647
1½ 1.50 6 1.3196
2 2.00 4½ 1.7594
*Data from ANSI B1.1: 1982. Equivalent to ISO 5864: 1993.
Fig. 5.2 Fastener dimensions
Engineers’ Guide to Rotating Equipment86
ISO metric screw threads (ISO 261)
The ISO thread profile is similar to the unified screw thread. They are
defined by a set of numbers and letters as shown in Fig. 5.3.
5.2 Bearings
Types
Bearings are basically subdivided into three types: sliding bearings (plane
motion), sliding bearings (rotary motion), and rolling element bearings (see
Fig. 5.4). There are three lubrication regimes for sliding bearings:
• boundary lubrication: there is actual physical contact between the surfaces;
• mixed-film lubrication: the surfaces are partially separated for intermittent
periods;
• full-film ‘hydrodynamic’ lubrication: the two surfaces ‘ride’ on a wedge of
lubricant.
Ball and roller bearings
Some of the most common designs of ball and roller bearings are shown in
Fig. 5.5. The amount of misalignment that can be tolerated is a critical factor
in design selection. Roller bearings have higher basic load ratings than
equivalent-sized ball types.
Bearing lifetime
Bearing lifetime ratings are used in purchasers’ specifications and
manufacturers’ catalogues and datasheets. The rating life (L10) is that
corresponding to a 10 per cent probability of failure and is given by:
L10 radial ball bearings = (Cr/Pr)3 × 106 revolutions
L10 radial roller bearings = (Cr/Pr)10/3 × 106 revolutions
L10 thrust ball bearings = (Ca/Pa)3 × 106 revolutions
L10 thrust roller bearings = (Ca/Pa)10/3 × 106 revolutions
M8 × 0.75 – 6g 8g
Nominal size in
millimeters (mm)
Pitch Tolerance
grade/position on
pitch diameter
Tolerance
grade/position on
crest diameter
Fig. 5.3 Typical ISO metric thread designation
Machine Elements 87
Radial
Bearings
Sliding bearings-plane motion-
Sliding bearings-rotary motion-
Axial
Hydrodynamic
Oil under pressure
Rolling element bearings
Ball Needle
Roller
Cylindrical Taper
Fig. 5.4 Bearing types
Engineers’ Guide to Rotating Equipment88
Cr and Ca are the static radial and axial load ratings that the bearing can
theoretically endure for 106 revolutions. Pr and Pa are corresponding
dynamic equivalent radial and axial loads.
So, as a general case:
roller bearings: L10 lifetime = [16700 (C/P)10/3]/n
ball bearings: L10 lifetime = [16700(C/P)3]/n
where
C = Cr or Ca
P = Pr or Pa as appropriate
n = speed in r/min
Fig. 5.5 Ball and roller bearings
Machine Elements 89
Coefficients of friction
The coefficient of friction between bearing surfaces is an important design
criterion for machine elements that have rotating, meshing, or mating parts.
The coefficient value (f) varies, depending on whether the surfaces are static
or already sliding, and whether they are dry or lubricated. Table 5.4 shows
some typical values.
Table 5.4 Typical friction (f) coefficients
Static (fo) Sliding (f)
Material Dry Lubricated Dry Lubricated
Steel/steel 0.75 0.15 0.57 0.10
Steel/cast iron 0.72 0.20 0.25 0.14
Steel/phosphor bronze – – 0.34 0.18
Steel/bearing ‘white metal’ 0.45 0.18 0.35 0.15
Steel/tungsten carbide 0.5 0.09 – –
Steel/aluminium 0.6 – 0.49 –
Steel/Teflon 0.04 – – 0.04
Steel/plastic – – 0.35 0.06
Steel/brass 0.5 – 0.44 –
Steel/copper 0.53 – 0.36 0.2
Steel/fluted rubber – – – 0.05
Cast iron/cast iron 1.10 – 0.15 0.08
Cast iron/brass – – 0.30 –
Cast iron/copper 1.05 – 0.30 –
Cast iron/hardwood – – 0.5 0.08
Cast iron/zinc 0.85 – 0.2 –
Hardwood/hardwood 0.6 – 0.5 0.17
Tungsten carbide/tungsten carbide 0.2 0.12 – –
Tungsten carbide/steel 0.5 0.09 – –
Tungsten carbide/copper 0.35 – – –
Note: The static friction coefficient between similar materials is high, and can result in
surface damage or seizure.
Engineers’ Guide to Rotating Equipment90
5.3 Mechanical power transmission –
broad guidelinesBecause of the large variety of types of rotating equipment that exist, the
basic characteristics of such equipment can vary greatly. One of the main
ways of classifying such equipment is by reference to its speed/
torque/power characteristics. Large heavy-duty machines such as kilns,
crushers, etc. have low-speed, high-torque characteristics whereas small
precision equipment lies at the opposite end of the scale, producing low
torque at high rotational speeds. Figure 5.6 shows some guidelines on the
speed/power/torque characteristics of a broad range of rotating equipment
types.
Machines that require a high-torque, low-speed output have to be matched
to their higher speed prime mover (diesel engine, electric motor, etc.) by a
speed reduction mechanism such as gears, chain/belt, or hydraulic drive.
Table 5.5 shows some guidelines on the characteristics of various types.
Fig. 5.6 Torque:speed relationships – broad guidelines
Machine Elements 91
Table 5.5 Speed reduction/torque increase mechanisms –
broad guidelines
Characteristic Gear drive Chain drive Belt drive Hydraulic drive
Maximum speed 60 m/s 14–17 m/s 25–60 m/s –
Maximum power 16–18 MW 600 kW 1200 kW 1200–1600 kW
capacity
Maximum torque 108 Nm 106 Nm 104 Nm 108 Nm
As a general ‘rule of thumb’, gear drives are more efficient than belt drives
and suffer less from vibration problems, but they are much less tolerant to
manufacturing inaccuracies and misalignment. Both gear and belt drives
provide a speed reduction ratio equivalent to the ratio of the radii of the
drive pair.
5.4 Shaft couplingsShaft couplings are used to transfer drive between two (normally co-axial)
shafts. They allow rigid, or slightly flexible, coupling depending on the
application. Figure 5.7 shows a typical ‘application chart’ for several
common types.
Bolted couplings
The flanges are rigidly connected by bolts, allowing virtually no
misalignment. Positive location may be achieved by using a spigot on the
flange face (see Fig. 5.8).
Bushed pin couplings
Similar to the normal bolted coupling, but incorporating rubber bushes in
one set of flange holes. This allows a limited amount of angular
misalignment (see Fig. 5.9).
Gear couplings
Gear couplings consist of involute-toothed hubs which mesh with an
intermediate sleeve or shaft (see Fig. 5.10). They allow significant amounts
of angular misalignment and axial movement. Figure 5.11 shows a typical
performance envelope, demonstrating the operational limitations of
rotational speed, power transmitted, gear tooth contact stress, and
centrifugal stress.
Engineers’ Guide to Rotating Equipment92
Fig. 5.7 Application chart of coupling types by factored
power and speed
Fig. 5.8 Solid bolted flange coupling
Machine Elements 93
Fig. 5.9 Rubber-bushed coupling
Fig. 5.10 A typical gear coupling
Simple disc-type flexible couplings
A rubber disc is bonded between thin steel discs held between the flanges
(see Fig. 5.12).
Membrane-type flexible couplings
These are used specifically for high-speed drives such as gas turbine
gearboxes, turbocompressors, and pumps. Two stacks of flexible steel
Engineers’ Guide to Rotating Equipment94
Fig. 5.11 Gear coupling performance envelope
Machine Elements 95
Fig. 5.12 Disc-type flexible coupling
Fig. 5.13 Typical membrane-type flexible couplings
Engineers’ Guide to Rotating Equipment96
diaphragms fit between the coupling and its mating input/output flanges.
These diaphragms are flexible in bending, but strong in tension and shear.
These couplings are installed with a static prestretch – the resultant axial
force varies with rotating speed and operating temperature. Figure 5.13
shows two common designs. The performance of these couplings is also
limited by centrifugal stress considerations. Figure 5.14 shows typical
performance envelopes.
Fig. 5.14 Performance envelopes for membrane-type
flexible couplings
Machine Elements 97
Complex-disc couplings
These are a more complicated version of the simple disc-type flexible
coupling, used in higher speed applications. Two sets of flexible discs are
fitted at either end of a central spacer tube (see Fig. 5.15). Figure 5.16
shows typical performance envelopes which exhibit centrifugal stress
limitations.
Balance of couplings
High-speed (and many low-speed) couplings need to be balanced to
minimize vibration effects. Table 5.6 shows some typical rules of thumb.
Fig. 5.15 Contoured disc coupling
Engineers’ Guide to Rotating Equipment98
Fig. 5.16 Performance envelopes for contoured disc coupling
Machine Elements 99
Table 5.6 Balance of couplings – some rules of thumb
• API 671 contains guidance on balance for ‘rigid’ couplings.
• A rigid coupling is one in which shaft bending does not significantly affect
the balance – it runs well below the first critical speed (i.e. N/Nc < 0.2
approximately).
• For non-API couplings, ISO 1940 is normally used (see Table 4.1).
Balance grade G16 is in common use for low-speed ‘rigid’ couplings.
• For flexible couplings that are defined as sub-critical, i.e. operating
speed/first critical speed N/Nc > about 0.2, the ISO 1940 balance grade
should be increased.
5.5 GearsGear trains are used to transmit motion between shafts. Gear ratios and
speeds are calculated using the principle of relative velocities. The most
commonly used arrangements are simple or compound trains of spur or
helical gears, epicyclic, and worm and wheel.
Simple trains
Simple trains have all their teeth on their ‘outside’ diameter (see Fig. 5.17).
Fig. 5.17 Simple gear train
Engineers’ Guide to Rotating Equipment100
Compound trains
Speeds are calculated as shown in Fig. 5.18.
Worm and wheel
A worm and wheel arrangement is used to transfer drive through 90 degrees,
usually incorporating a high gear ratio and output torque. The wheel is a
helical gear, see Fig. 5.19.
Fig. 5.18 Compound gear train
Machine Elements 101
Spur gears
Spur gears are the simplest form of gearing arrangement used to transmit
power between shafts rotating at (usually) different speeds (see Fig. 5.20).
In most applications, spur gear sets are used for speed reduction, i.e. the
power is transmitted from a high-speed, low-torque input shaft to a low-
speed, high-torque output shaft. Compound trains may also be used.
Fig. 5.19 Worm and wheel
Fig. 5.20 Spur gears
Engineers’ Guide to Rotating Equipment102
Tooth geometry and kinetics
Spur gear teeth extend from the root or ‘dedendum’ circle to the tip or
‘addendum’ circle (see Fig. 5.21). The ‘face’ or ‘flank’ is the portion of the
tooth that provides the ‘drive’ contact to the mating gear. The root region
contains a fillet to reduce fatigue stresses, and a root clearance.
For kinetic analysis purposes, spur gears are regarded as equivalent pitch
cylinders which roll against each other without any slip. Note that the pitch
cylinder diameter is a ‘theoretical’ dimension.
Other key parameters for spur gear sets are:
• Circular pitch p = distance between adjacent teeth around
the pitch circle
z = number of teeth on a gear of pitch
diameter D
• Module m = a measure of size = p/π ; the module
must be the same for both gears in a
meshing set
• Pitch point P = a ‘theoretical’ point at which the pitch
circles of the gears contact each other
Fig. 5.21 Tooth geometry
Machine Elements 103
• Pitch line velocity v = the velocity of the pitch point, P
• Tangential force Pt = the tangential force component at the
component pitch point P resulting from the meshing
contact between the gears; it is this force
component that transfers the power
• Radial force component Pr = the radial force component (i.e. plays no
part in the power transfer)
• Axial force component Pa = force acting axially along the direction
of the gear shaft; it is zero for spur gears
Double helical gears
These are used in most high-speed gearboxes. The double helices produce
opposing axial forces that cancel each other out (see Figs 5.22 and 5.23).
Fig. 5.22 Double helical gears
Engineers’ Guide to Rotating Equipment104
Epicyclic gear sets
An epicyclic gear set consists of internal and external gears, assembled into
a concentric set. They are used when a high speed or torque ratio has to be
achieved in a compact physical space. Various arrangements are possible,
depending on whether internal or external gears are used and which parts of
the gear assembly are held stationary. Figure 5.24(a) shows a ‘sun and
planet’ arrangement in which the planet gear rotates freely on its axle.
Figure 5.24(b) shows a different arrangement in which the central ‘sun’ gear
is replaced by a large-diameter internal ring-gear.
Figure 5.25 shows a typical physical layout of a basic epicyclic gearbox.
Pa
Pa
Pa
Fig. 5.23 Double helical gears: forces
Pa = axial force
from gear
Machine Elements 105
Fig. 5.24 Epicyclic – sun and planet arrangements
(a)
(b)
Engineers’ Guide to Rotating Equipment106
Tooth geometry and kinetics
Figure 5.24 shows torque and tangential force components, Pt, as they act on
each of the gear components, represented as ‘free body diagrams’. Note that
each element has a single degree of ‘kinetic’ (torque) freedom, but two
degrees of kinematic freedom. Key equations used in analyses are:
• (ωc – ωa)zc + (ωp – ωa)zp = 0
• Tc /zc = Tp /zp =
where zc is a positive integer for an external central gear and a negative
integer for an internal central gear.
ωc = angular velocity of central gear
ωp = angular velocity of planet gear
ωa = angular velocity of connecting arm
Tc = torque on central gear shaft
Tp = torque on planet gear itself
Ta = torque on connecting arm
Fig. 5.25 Basic epicyclic gearbox layout
a
c p
–
( + )
T
z z
Machine Elements 107
Gear selection
Table 5.7 shows basic information on gear selection of various rotating
equipment applications.
Table 5.7 Gear selection – basic information
Type Features Applications Comments regarding
precision
Spur • Parallel
shafting
Applicable to all
types of trains
and a wide
range of
velocity ratios.
Simplest tooth elements
offering maximum
precision. Suitable for all
gear meshes, except
where very high speeds
and loads or special
features of other types,
such as right angle drive,
cannot be avoided.
• High speeds
and loads
• Highest
efficiency
Helical • Parallel
shafting
Most applicable
to high speeds
and loads.
Equivalent quality to
spurs except for
complication of helix
angle. Suitable for all
high-speed and high-load
meshes. Axial thrust
component must be
accommodated.
• Very high
speeds and
loads
• Efficiency
slightly less
than spur
mesh
Crossed-
helical
• Skewed
shafting
Relatively low
velocity ratio;
low speeds and
light loads only.
Any-angle skew
shafts.
Not suitable for precision
meshes. Point contact
limits capacity and
precision. Suitable for
right-angle drives under
light load. Good
lubrication essential
because of point contact
and high sliding action.
• Point contact
• Low speeds
• Light loads
Engineers’ Guide to Rotating Equipment108
Gear nomenclature
Gear standards refer to a large number of critical dimensions of the gear
teeth. These are controlled by tight manufacturing tolerances.
Gear materials
Table 5.8 shows basic information on applications of gear materials.
Internal
spur
• Parallel
shafts
Internal drives
requiring high
speeds and
high loads;
offers low
sliding and high
stress loading.
Used in
planetary gears
to produce
large reduction
ratios.
Not suitable for precision
meshes because of
design, fabrication, and
inspection limitations.• High speeds
• High loads
Bevel • Intersecting
shafts
Suitable for 1:1
and higher
velocity ratios
and for right-
angle meshes.
Suitable for right-angle
drive, particularly low
ratios. Complicated tooth
form and fabrication
limits achievement of
precision.
• High speeds
• High loads
Worm
mesh
• Right-angle
skew shafts
High velocity
ratio.
Angular
meshes.
High loads.
Worm can be made to
high precision, but the
worm gear has inherent
limitations. Suitable for
average precision
meshes. Best choice for
combination high velocity
ratio and right-angle
drive. High sliding
requires adequate
lubrication.
• High velocity
ratio
• High speeds
and loads
• Low
efficiency
Table 5.7 Cont.
Machine Elements 109
Table 5.8 Gear materials – basic information
Material Features Application
Ferrous
Cast irons Low cost, good machining,
high internal damping.
Large-size, moderate
power rating commercial
gears.
Cast steels Low cost, high strength. Power gears, medium
ratings.
Plain-carbon
steels
Good machining, heat
treatable.
Power gears, medium
ratings.
Alloy steels Heat treatable, highest
strength and durability.
Severest power
requirements.
Stainless steels
AISI 300 series High corrosion resistance,
non-magnetic, non-
hardenable.
Extreme corrosion, low
power ratings.
AISI 400 series Hardenable, magnetic
moderate stainless steel
properties.
Low to medium power
ratings, moderate
corrosion.
Non-ferrous
Aluminium alloys Light weight, non-corrosive,
excellent machinability.
Extremely light duty
instrument gears.
Brass alloys Low cost, non-corrosive,
excellent machinability.
Low-cost commercial
equipment.
Bronze alloys Excellent machinability, low
friction, and good
compatibility with steel
mates.
Mates for steel power
gears.
Magnesium alloys Extremely light weight,
poor corrosion resistance.
Special lightweight, low-
load uses.
Nickel alloys Low coefficient of thermal
expansion, poor
machinability.
Special thermal cases.
Titanium alloys High strength for moderate
weight, corrosion resistant.
Special lightweight
strength applications.
Die-cast alloys Low cost, no precision, low
strength.
High production, low
quality, commercial.
Sintered powder
alloys
Low cost, low quality,
moderate strength.
High production, low
quality commercial.
Engineers’ Guide to Rotating Equipment110
Table 5.9 shows gear forces for various types of gear.
5.6 SealsSeals are used either to provide a seal between two working fluids or to
prevent leakage of a working fluid to the atmosphere past a rotating shaft.
There are several types.
Bellows seal
This uses a flexible bellows to provide pressure and absorb misalignment
(see Fig. 5.26).
Labyrinth gland
This consists of a series of restrictions formed by projections on the shaft
and/or casing (see Fig. 5.27). The pressure of the steam or gas is broken
down by expansion at each restriction. There is no physical contact between
the fixed and moving parts.
Mechanical seals
Mechanical seals are used either to provide a seal between two working
fluids or to prevent leakage of a working fluid to the atmosphere past a
rotating shaft. This rotary motion is a feature of mechanical seals. Other
types of seal are used for reciprocating shafts, or when all the components
are stationary. Figure 5.28 shows a typical mechanical seal and Fig. 5.29 a
specific design with its component pieces. They can work with a variety of
fluids and, in the extreme, can seal against pressures of up to 500 bar, and
have sliding speeds of more than 20 m/s. The core parts of the seal are the
rotating ‘floating’ seal ring and the stationary seat. Both are made of wear-
resistant materials and the floating ring is kept under axial force from a
Non-metallic
Delrin Wear resistant, long life,
low water absorption.
Long life, low noise, low
loads.
Phenolic
laminates
Quiet operation, highest
strength plastic.
Medium loads, low
noise.
Nylons Low friction, no lubricant,
high water absorption.
Long life, low noise, low
loads.
Teflon
(flurocarbon)
Low friction, no lubricant. Special low friction.
Table 5.8 Cont.
Machin
e E
lem
ents
111
( ) δ∝t AV
tan sinP
( ) [ ]δ β δβ
∝ ±t AVAV
AV
tan sin sin coscos
P
t
2
2M
d
β∝
t
tan
cosP
β∝
t
tan
cosP
( ) δ∝t AV
tan cosP
( ) [ ]δ β δβ
∝ ±t AVAV
AV
tan cos sin sincos
P
t
1
2M
d
t
1
2M
d
t
1
2M
d
( )
( )
=
=−
t
t AVAV
t
1
2
2
1 0.5 /
MP
d
M
d b R
( )
( )
=
=−
tt AV
AV
t
1
2
2
1 0.5 /
MP
d
M
d b R
t
2
2M
d
Tangential
force Pt
Radial
force Pr
Axial force
Pa
Spur
Herringbone
Helical
Spiral
Straight
Worm
Wheel
Cylindrical
gears
Bevel
gears
Worm
gears
Table 5.9 Formulae for gear forces
Pt tan ∝
Pt tan β
Pt tan ∝
Pt tan ∝P1tan (γ + p)
Pt tan (γ + p)
Engineers’ Guide to Rotating Equipment112
Fig. 5.26 Bellows seal
Fig. 5.27 Labyrinth gland
Fig. 5.28 Mechanical seal
Machine Elements 113
spring or bellows to force it into contact with the seat face. This is the most
common type and is termed a ‘face seal’. It is found in common use in many
engineering applications: vehicle water pumps and automatic transmission
gearboxes, washing machines and dishwashers, as well as more traditional
industrial use on most types of process pumps. Materials of construction are
quite varied, depending on the characteristics of the process fluid.
Fig. 5.29 Mechanical seal
Engineers’ Guide to Rotating Equipment114
Table 5.10 Mechanical seal notation
A Seal area ratio
Ah Hydraulic area
Ai Interface area
b Seal interface width
C A ‘shape factor’
d Internal diameter of seal interface
dh Recess diameter
D External diameter of seal interface
E Young’s modulus of seal ring
M Moment arm
P Sealed fluid pressure (external)
pi Sealed fluid pressure (internal)
r Internal radius of a ring
rm Mean radius of seal interface
rp Torque arm radius
R External radius of a ring
s Deflection of seal ring
Wf Friction force
Wh Net hydraulic force
Wo Opening force
Ws Spring force
σb Compressive stress at seal ring bore
σz Tensile stress at seal ring bore
φ Angular distortion of ring
Table 5.10 shows typical mechanical seal notation.
Mechanical seals are mass-produced items manufactured in a large range of
sizes. Special designs are required for use with aggressive process fluids
such as acids, alkalis, and slurries. The design of mechanical seals is
specialized and has developed iteratively over many years using a mixture
of engineering disciplines such as:
• Thermodynamics. Heat transfer in the seal components and the fluid film
must be considered.
• Fluid mechanics. Hydrodynamic, boundary, and static lubrication
conditions exist in various areas of the sealing face and associated parts
of the seal assembly. Laminar flow calculations govern the leakage path
between the floating seal ring and stationary seat. Static fluid pressure
considerations are used to determine the additional axial ‘sealing force’
generated by the process fluid.
Machine Elements 115
• Deformable body mechanics. Deformation of the seal ring in use is an
important design parameter. This is calculated using classical ‘hollow
cylinder’ assumptions with ‘open-end’ boundary conditions. Local
deformations of the seal and seat faces are important (see Fig. 5.30).
• Surface mechanics. Surface characteristics, particularly roughness
profile, of the contacting faces affect leakage, friction, and wear. This
plays an important part in the tribology (the study of moving surfaces in
contact) of the sealing faces.
• Materials technology. Material properties also play a part in the tribology
of mechanical seals. The compatibility of the seal faces, wear resistance,
and friction characteristics are influenced by the choice of materials –
many seals use very specialized wear-resistant materials such as plastics
or ceramics.
Fig. 5.30 Mechanical seal ring behaviour
Engineers’ Guide to Rotating Equipment116
Seal area ratio
In practice, most mechanical seals do not rely only on the force of the spring
to keep the seal faces in contact (termed ‘closure’). Closure is mainly
achieved by the net hydraulic fluid pressure acting on the seal floating ring.
This net hydraulic pressure is a function of the differential areas of the
floating ring – hence the closure force increases as the sealed fluid pressure
increases, and the spring actually plays little part. Figure 5.30 shows how
the closure force is made up of four components. The net hydraulic force Wh
comes from the sealed fluid at pressure pi. This is joined by the spring force
Ws, the ‘opening’ force Wo caused by the seal interface fluid pressure, and
the friction force Wf caused by the frictional resistance of the static seal.
Opening force Wo is normally calculated using the assumption that fluid
pressure varies in a linear way across the radial seal face. The frictional
resistance force Wf is just about indeterminable and is often ignored. Note
the locations of the static ‘O’ ring seals; they are an essential part of the seal
assembly, to eliminate static leakage paths.
Seal ring dimensions
Mechanical seal design includes static calculations on the seal rings, which
must have a sufficient factor of safety to avoid bursting. A valid assumption
used is that face seal rings behave as hollow cylinders with open ends.
Hence, for a hollow cylinder with internal radius r, external radius R, subject
to internal pressure pi and external pressure P it can be shown that
Maximum stress (Lamé)
For internal pressure (i.e. when P = 0) then maximum tensile stress, σz, at
the ring bore is given by
or, for external pressure (i.e. where pi = 0), then maximum compressive
stress σb at the bore is given by
These equations only apply, strictly, to seal rings of plain rectangular cross-
section. They can be used as an order-of-magnitude check, however; then
significant factors of safety are included to allow for any uncertainties.
2 2 2i
2 2
( ) 2p R r PR
R rσ + −=
−
2 2i
z 2 2
( )p R r
R rσ +=
−
( )b 2
2
1
P
rR
σ =−
Machine Elements 117
Seal ring deflections
A further important design criterion is the twisting moment which occurs in
the floating seal ring. This can cause deflection (distortion) of the seal ring
surface. From Figs 5.29 and 5.30:
D = external diameter of seal interface
d = internal diameter of seal interface
dh = recess diameter
rm = mean radius = (D + d)/4
rp = torque arm radius
b = seal interface width
The moment arm M = P(rp – rm)
where
P = AP b
and
rp =
As the area ratio A tends towards being greater or smaller than unity then the
lever distance (rp – rm) gets larger, hence increasing the moment M. This
moment produces angular distortion of the floating seal ring. Referring
again to Fig. 5.30 the angular distortion φ is given by
This results in a physical deflection s given by
s = φbC
where C is a shape factor (near unity) related to the section of the floating
ring.
The result of this is that the floating ring will contact at one end of its
surface. As a general rule for rings under external pressure:
• if A < 1, the floating ring twists ‘inwards’ towards the shaft and hence
contacts at its outer ‘D’ edge.
• if A > 1, the floating ring twists ‘outwards’ away from the shaft and hence
contacts at its inner ‘d’ edge.
It is essential, therefore, when considering seal design, to calculate any
likely twist of the floating seal rings to ensure that this is not so excessive
that it reduces significantly the seal interface contact area. A maximum
distortion s of 15 microns is normally used as a rule of thumb.
d
4
hD +
m
3
12
( / )
Mr
El R rφ =
Engineers’ Guide to Rotating Equipment118
Friction considerations
The floating seal ring/seat interface is the main area of a mechanical seal in
which friction is an issue. The whole purpose of this interface is to provide
the main face sealing surface of the assembly with only a controlled degree
of leakage, hence some friction at this face is inevitable. If it becomes too
high, too much heat will be generated, which may cause excessive distortion
of the components and eventual seizure. Given that rotational speed of the
shaft is difficult to change (it is decided by the process requirements of the
pump or machine) careful choice of the ring materials and their respective
surface finish is the best way of keeping friction under control.
Surface finish is defined using the parameter Ra measured in microns.
This is the average distance between the centreline of a surface’s
undulations and the extremes of the peaks and the troughs. It is sometimes
referred to as the centre line average (CLA); see Chapter 11, Fig. 11.9. If the
surface is too rough, the effective contact area of the interface will be
reduced, resulting in a significant increase in seal loading for a constant
closure force W. This can cause lubrication film breakdown and seizure.
Experience shows that the lubrication regime existing between the interface
surfaces is rarely completely hydrodynamic; boundary lubrication
conditions provide a better assumption and these are prone to breakdown if
specific contact loading is too high. Conversely, a surface that is too smooth
is less able to ‘hold’ the lubricant film so, while the effective contact area of
the interface is increased with smooth surfaces, there may be negative
effects on the stability of the lubrication regime. In practice it has been
found that a surface roughness of 0.1 ± 0.025 µm Ra (both contacting rings)
gives the best results.
Assembly considerations
Many mechanical seals fail in the early stages of their life because of
inaccurate assembly. This is normally due to one of two reasons.
• Axial misalignment. This is displacement of the seal end housing, and/or
the static seat sealing ring so that its centreline lies at an angle to that of
the rotating parts. This results in almost instantaneous wear and failure
after only a few running hours. Misalignment can be prevented by
incorporating features that give positive location of the seal end housing.
• Poor concentricity. This is mainly a fault with the positioning of the fixed
seal seating ring centreline, i.e. it is not concentric with that of the shaft.
It can be almost eliminated by specifying the manufactured concentricity
level of the components and then providing a positive concentric location
for the seal seating ring in the end housing. Note that this must still
incorporate the ‘O’ ring, which prevents fluid leakage.
Machine Elements 119
To avoid sharp changes in section of the rotating shaft, while still providing
an abutment face for the closure spring, some seal designs incorporate a
shaft sleeve. This fits concentrically over the shaft for slightly more than the
length of the spring. The static ‘O’ ring rubber seals are often a problem
during assembly as they can be chafed by the sharp edges of their slots. This
causes the ‘O’ ring to lose its 100 per cent sealing capability.
5.7 Cam mechanismsA cam and follower combination are designed to produce a specific form of
output motion. The motion is generally represented on a displacement/time
(or lift/angle) curve. The follower may have a knife-edge, roller, or flat
profile.
Constant velocity cam
This produces a constant follower speed and is only suitable for simple
applications (see Fig. 5.31).
Fig. 5.31 Constant velocity cam
Engineers’ Guide to Rotating Equipment120
Uniform acceleration cam
The displacement curve is a second-order function giving a uniformly
increasing/decreasing gradient (velocity) and constant d2x/dt2 (acceleration).
See Fig. 5.32.
Simple harmonic motion cam
A simple eccentric circle cam with a flat follower produces simple harmonic
motion (see Fig. 5.33).
Fig. 5.32 Uniform acceleration cam
Machine Elements 121
The motion follows the general harmonic motion equation
d2x/dt2 = –ω2x
where
x = displacement
ω = angular velocity
T = periodic time
dx/dt = –ωa sin ωt
T = 2π/ω
5.8 Belt drives
Types
The most common types of belt drive are flat, ‘V’, wedge, and ribbed (see
Fig. 5.34).
• Flat belts are weak and break easily – their use is limited to a few low-
torque high-speed applications.
• ‘V’ belts provide a stronger and more compact drive than a flat belt and
comprise cord tensile strands embedded in the matrix of the belt material,
in the region of the pitchline.
Fig. 5.33 Simple harmonic motion cam
Engineers’ Guide to Rotating Equipment122
• A variant of the ‘V’ belt is the lighter and narrower wedge belt. The lighter
weight means that centrifugal forces (which reduce the driving friction of
the belt in the pulley grooves) are lower, hence the belt provides better
drive at higher speeds than a plain ‘V’ belt.
• A further variant is the cogged wedge belt – this uses transverse slots or
recesses on the underside of the belt to enable the belt to bend more easily
around smaller diameter pulleys. The slots play little or no effective part
in the driving action.
• The most advanced type of belt drive is the toothed belt, which gives a
positive drive using gear-like teeth.
For higher power transmission requirements, multiple or ganged belts are
used on multi-grooved pulleys. All belts are manufactured in a range of
standard cross-sectional sizes carrying various designations.
Fig. 5.34 Belt drive types
Machine Elements 123
‘V’ belt geometry
The main use for ‘V’ belts is in short-centre drives with speeds of around
20 m/s. Figure 5.35 shows an indicative range of size/power characteristics
and Fig. 5.36 the basic geometry of the drive.
5.9 ClutchesClutches are used to enable connection and disconnection of driver and
driven shafts.
Jaw clutch
One half of the assembly slides on a splined shaft. It is moved by a lever
mechanism into mesh with the fixed half on the other shaft. The clutch can
only be engaged when both shafts are stationary. Used for crude and slow-
moving machines such as crushers (see Fig. 5.37).
Cone clutch
The mating surfaces are conical and normally lined with friction material.
The clutch can be engaged or disengaged when the shafts are in motion.
Used for simple pump drives and heavy duty materials handling equipment
(see Fig. 5.38).
Multi-plate disc clutch
Multiple friction-lined discs are interleaved with steel pressure plates. A
lever or hydraulic mechanism compresses the plate stack together.
Universal use in motor vehicles with manual transmission (see Fig. 5.39).
Fluid couplings
Radial-vaned impellers run in a fluid-filled chamber. The fluid friction
transfers the drive between the two impellers. Used in automatic
transmission motor vehicles and for larger equipment such as radial fans and
compressors (see Fig. 5.40).
The key design criterion of any type of friction clutch is the axial force
required in order to prevent slipping. A general formula is used, based on the
assumption of uniform pressure over the contact area (see Fig. 5.41).
T = torque
f = coefficient of friction
2 22 1
3 3
2 1
3 ( )Force =
2 ( )
T r rF
f r r
−−
Engineers’ Guide to Rotating Equipment124
Fig. 5.35 ‘V’/wedge belts – indicative size:power
characteristics
Machine Elements 125
C = Centre distance
v = Belt speed
R = Drive ratio ≡ D2/D1
θ1 = θ2 = wrap angle on each pulley = π–2γβ = Belt grove ‘semi’ angle ≅ 16–20°
Fig. 5.36 ‘V’/wedge belts – basic geometry
Engineers’ Guide to Rotating Equipment126
Fig. 5.37 Jaw clutch
Fig. 5.38 Cone clutch
Fig. 5.39 Multi-plate disc clutch
Machine Elements 127
Fig. 5.40 Fluid coupling
Fig. 5.41 Clutch friction
Engineers’ Guide to Rotating Equipment128
5.10 Brakes
Brake types
Brakes are used to decelerate a rotating component or system of components
by absorbing power from it. Most types use simple sliding friction. Figure
5.42 shows some basic models.
• The simple band brake comprises a flexible band bearing on the
circumference of a drum; these are used on simple winches.
• The external shoe brake has external shoes with friction linings, rigidly
connected to pivoted posts. The brake is operated by a linkage, which
provides an actuation force, pulling the brake shoes into contact with the
drum.
• Internal drum brakes, used on older designs of motor vehicle, operate by
the friction-lined brake shoes being pushed into contact with the internal
surface of a brake drum by a single cam (leading/trailing leading shoe
type) or twin hydraulic cylinders (twin leading shoe type).
• Hydraulic disc brakes, as found on most road vehicles, aircraft, etc. and
many industrial applications comprise twin opposing hydraulic pistons
faced with pads of friction material. The pads are forced into contact with
the disc by hydraulic pressure, exerting forces normal to the disc which
transfer into tangential friction forces, thereby applying a deceleration
force to the disc.
5.11 Pulley mechanismsPulley mechanisms can generally be divided into either ‘simple’ or
‘differential’ types.
Simple pulleys
These have a continuous rope loop wrapped around the pulley sheave. The
key design criterion is the velocity ratio (see Fig. 5.43).
Velocity ratio, VR = the number of rope cross-sections supporting the load.
Differential pulleys
These are used to lift very heavy loads and consist of twin pulleys ‘ganged’
together on a single shaft (see Fig. 5.44).
2 2 = =
( )
R RVR
R r R r
ππ − −
Machine Elements 129
Fig. 5.42 Brakes – basic types
Engineers’ Guide to Rotating Equipment130
Fig. 5.43 Simple pulleys
Fig. 5.44 Differential pulleys
Machine Elements 131
5.12 Useful references and standards
Standards: bearings
1. BS 5983 Part 6: 1983 Metric spherical plain bearings – glossary of
terms.
2. BS 5512: 1991 Method of calculating load ratings and rating life of
roller bearings. This is an equivalent standard to ISO 281.
3. BS 292: Part 1: 1987 Specification for dimensions of ball, cylindrical
and spherical roller bearings (metric series).
4. BS 5645: 1987 Glossary of terms for roller bearings. Equivalent to ISO 76.
5. BS 5989: Part 1: 1995 Specification for dimensions of thrust bearings.
Equivalent to ISO 104: 1994.
6. BS 6107 (various parts). Rolling bearings – tolerances.
7. BS ISO 5593: 1997 Rolling bearings – vocabulary.
8. ABMA A24.2: 1995 Bearings of ball, thrust and cylindrical roller types
– inch design.
9. ABMA A20: 1985 Bearings of ball, radial, cylindrical roller, and
spherical roller types – metric design.
10. ISO 8443: 1989 Rolling bearings.
11. ANSI/ABMA/ISO 5597: 1997 Rolling bearings – vocabulary.
Bearing websites
1. Anti-Friction Bearing Manufacturers Association Inc: www.afbma.org
2. www.skf.se/products/index.htm
3. www.nsk-ltd.co.jp
Standards: gears
1. ISO 1328: 1975 Parallel involute gears – ISO system of accuracy.
2. ANSI/AGMA 2000-A88 1994 Gear classification and inspection
handbook.
3. ANSI/AGMA 6002: B93 1999 Design guide for vehicle spur and helical
gears.
4. ANSI/AGMA 6019-E89: 1989 Gear-motors using spur, helical
herringbone straight bevel, and spiral bevel gears.
5. BS 436: Part 1: 1987 Basic rack form, pitches, and accuracy.
6. API 613: 1998 Special-purpose gear units for refinery service.
7. DIN 3990: 1982 Calculation of load capacity of cylindrical gears.
Engineers’ Guide to Rotating Equipment132
Gear websites
1. www.agma.org
2. www.Reliance.co.uk
3. www.flender.com
Standards: seals
Mechanical seals are complex items and manufacturers’ in-house
(confidential) standards tend to predominate. Some useful related standards
are:
1. MIL S-52506D: 1992 Mechanical seals for general purpose use.
2. KS B1566: 1997 Mechanical seals.
3. JIS (Japan) B2405: 1991 Mechanical seals – general requirements.
4. BS 6241: 1982 Specification of housings for hydraulic seals for
reciprocating applications. This is a similar standard to ISO 6547.
Seal websites
1. www.flexibox.com
2. www.garlock-inc.com
Standards: couplings
1. BS 6613: 1991 Methods of specifying characteristics of resilient shaft
couplings. Equivalent to ISO 4863.
2. BS 3170: 1991 Specification for flexible couplings for power trans-
mission.
3. BS 5304: 1988 Code of practice for safety of machinery. This includes
details on the guarding of shaft couplings.
4. API 617: 1990 Special-purpose couplings for refining service.
5. AGMA 515 Balance classification for flexible couplings.
6. KS B1555 Rubber shaft couplings.
7. KS B1553 Gear type shaft couplings.
8. ISO 10441: 1999 Flexible couplings for mechanical power trans-
mission.
9. ANSI/AGMA 9003-A91 (R1999) Flexible couplings – keyless fits.
Standards: clutches
1. BS 3092: 1988 Specification for main friction clutches for internal
combustion engines.
2. SAE J2408: 1984 Clutch requirements for truck and bus engines.
Machine Elements 133
Standards: pulleys
1. SAE J636: 1992 ‘V’ belts and pulleys.
2. BS 3876: Part 2: 1990 Specification for vertical spindle pulleys,
mountings and assemblies.
Standards: belt drives
1. BS 7620: 1993 Specification for industrial belt drives – dimensions of
pulleys and ‘V’ribbed belts of PH, PJ, PK, PL, and PM profiles. Similar
to ISO 9982.
2. BS 4548: 1987 Specification for synchronous belt drives for industrial
applications. Similar to ISO 5294.
3. BS AU 150b: 1990 Specification for automotive ‘V’ belts and pulleys.
4. BS AU 218: 1987 Specification for automotive synchronous belt drives.
5. SAE J637: 1998 ‘V’ belt drives.
6. RMA-IP20: 1987 Specification for drives – ‘V’ belt and sheaves.
7. ISO 22: 1991 Belt drives – flat transmission belts.
8. ISO 4184: 1992 Belt drives – classical and narrow ‘V’ belts.
CHAPTER 6
Fluid Mechanics
6.1 Basic properties
Basic relationships
Fluids are classified into liquids, which are virtually incompressible, and
gases, which are compressible. A fluid consists of a collection of molecules
in constant motion: a liquid adopts the shape of a vessel containing it, while
a gas expands to fill any container in which it is placed. Some basic fluid
relationships are given in Table 6.1.
Table 6.1 Basic fluid relationships
Density, ρ Mass per unit volume. Units kg/m3 (lb/in3)
Specific gravity, s Ratio of density to that of water, i.e. s = ρ/ρwater
Specific volume, v Reciprocal of density, i.e. v = 1/ρ. Units m3/kg (in3/lb)
Dynamic viscosity, µ A force per unit area or shear stress of a fluid. Units
Ns/m2 (lbf.s/ft2)
Kinematic viscosity, ν A ratio of dynamic viscosity to density, i.e. ν = µ/ρ.
Units m2/s (ft2/s)
Perfect gas
A perfect (or ‘ideal’) gas is one that follows Boyle’s/Charles’s law
pv = RT
where
Engineers’ Guide to Rotating Equipment136
p = pressure of the gas
v = specific volume
T = absolute temperature
R = the universal gas constant
Although no actual gases follow this law totally, the behaviour of most gases
at temperatures well above their liquification temperature will approximate
to it and so they can be considered as a perfect gas.
Changes of state
When a perfect gas changes state its behaviour approximates to
pvn = constant
where n is known as the polytropic exponent.
The four main changes of state relevant to rotating equipment are:
isothermal, adiabatic, polytropic, and isobaric.
Compressibility
The extent to which a fluid can be compressed in volume is expressed using
the compressibility coefficient β.
where
∆v = change in volume
v = initial volume
∆p = change in pressure
K = bulk modulus
Also
and
where
a = the velocity of propagation of a pressure wave in the fluid.
/ 1v v
p K
∆β∆
= =
dp Ka
d ρ ρ = =
√ √
p dpK
d
∆ρ ρ∆ρ ρ
= =
Fluid Mechanics 137
Fluid statics
Fluid statics is the study of fluids that are at rest (i.e. not flowing) relative to
the vessel containing them. Pressure has four important characteristics:
• pressure applied to a fluid in a closed vessel (such as a hydraulic ram) is
transmitted to all parts of the closed vessel at the same value (Pascal’s
law);
• the magnitude of pressure force acting at any point in a static fluid is the
same, irrespective of direction;
• pressure force always acts perpendicular to the boundary containing it;
• the pressure ‘inside’ a liquid increases in proportion to its depth.
Other important static pressure equations are:
• absolute pressure = gauge pressure + atmospheric pressure
• pressure p at depth h in a liquid is given by
p = ρgh
• a general equation for a fluid at rest is
This relates to an infinitesimal vertical cylinder of fluid.
6.2 Flow equationsFluid flow in rotating equipment may be one-dimensional (1-D), two-
dimensional (2-D), or three-dimensional (3-D) depending on the way that
the flow is constrained.
One-dimensional flow
One-dimensional flow has a single direction co-ordinate x and a velocity in
that direction of v. Flow in a pipe or tube is generally considered one-
dimensional. The equations for 1-D flow are derived by considering flow
along a straight stream tube (see Fig. 6.1). Table 6.2 shows the principles,
and their resulting equations.
dd d d 0
d
ppdA p A g A z
zρ − + − =
Engineers’ Guide to Rotating Equipment138
The stream tube for conservation of mass
The stream tube and element for the momentum equation
The forces on the element
Control volume for the energy equation
Fig. 6.1 One-dimensional flow
Fluid Mechanics 139
Table 6.2 Fluid principles
Two-dimensional flow
Two-dimensional flow (as in the space between two parallel flat plates) is
that in which all velocities are parallel to a given plane. Either rectangular
(x,y) or polar (r,θ) co-ordinates may be used to describe the characteristics
of 2-D flow. Table 6.3 and Fig. 6.2 show the fundamental equations.
Law Basis Resulting equations
Conservation
of mass
Matter (in a stream tube or
anywhere else) cannot be
created or destroyed.
Conservation
of momentum
The rate of change of
momentum in a given
direction = algebraic sum
of the forces acting in that
direction (Newton's second
law of motion).
Conservation
of energy
Energy, heat and work are
convertible into each other
and are in balance in a
steadily operating system.
Equation of
state
Perfect gas state p/ρT = R
and the first law of
thermodynamics
ρvA = constant
= constant
This is Bernoulli’s equation
212
dpv gz
ρ + + ∫√
constant for an
adiabatic (no heat
transferred) flow system
2
2p
vc T + =
p = kργ
k = constant
γ = ratio of specific heats cp/cv
Engineers’ Guide to Rotating Equipment140
Table 6.3 Two-dimensional flow – fundamental equations
Basis The equation Explanation
Laplace’s equation
or
where
Equation of motion
in 2-D
Equation of
continuity in 2-D
(incompressible
flow) or, in polar,
Equation of vorticity
or, in polar,
Stream function ψ Velocity at a point is
(incompressible given by
flow)
Velocity potential φ Velocity at a point is φ is defined as
(irrotational 2-D given byφ = cos β ds
flow)
A flow described by a
unique velocity potential is
irrotational.
The principle of force =
mass × acceleration
(Newton’s law of motion)
applies to fluids and fluid
particles.
If fluid velocity increases
in the x direction, it must
decrease in the y
direction.
A rotating or spinning
element of fluid can be
investigated by assuming
it is a solid.
ψ is the stream function.
Lines of constant ψ give
the flow pattern of a fluid
stream.
φ φ ψ ψ∂ ∂ ∂ ∂+ = = +∂ ∂ ∂ ∂
2 2 2 2
2 2 2 20
x y x y
φ ψ∇ = ∇ =2 2 0
∂ ∂∇ = +∂ ∂
2 22
2 2x y
ρ∂ ∂ ∂ ∂ + + = − ∂ ∂ ∂ ∂
1u u u pu v X
t x y x
ρ ∂ ∂ ∂ ∂+ + = − ∂ ∂ ∂ ∂
1v v v pu v Y
t x t y
∂ ∂+ =∂ ∂
0u v
x y
θ∂∂+ + =
∂ ∂1
0tn nqq q
r r r
ς∂ ∂− =∂ ∂v u
x y
ςθ
∂ ∂= + −∂ ∂
1t t nq q q
r r r
ψ ψ∂ ∂= = −∂ ∂
u vy x
φ φ∂ ∂= =∂ ∂
u vx y
∫op
q
Fluid Mechanics 141
Rectangular co-ordinates
Polar co-ordinates
Fig. 6.2 Two-dimensional flow
Engineers’ Guide to Rotating Equipment142
The Navier–Stokes equations
The Navier–Stokes equations are written as
Sources and sinks
A ‘source’ is an arrangement where a volume of fluid, +q, flows out evenly
from an origin toward the periphery of an (imaginary) circle around it. If q
is negative, such a point is termed a ‘sink’ (see Fig. 6.3). If a source and sink
of equal strength have their extremities infinitesimally close to each other,
while increasing the strength, this is termed a ‘doublet’.
6.3 Flow regimes
General descriptions
Flow regimes can be generally described as follows (see Fig. 6.4):
• Steady flow Flow parameters at any point do not vary with time
(even though they may differ between points).
• Unsteady flow Flow parameters at any point vary with time.
• Laminar flow Flow which is generally considered smooth, i.e. not
broken up by eddies.
• Turbulent flow Non-smooth flow in which any small disturbance is
magnified, causing eddies and turbulence.
• Transition flow The condition lying between laminar and turbulent flow
regimes.
Reynolds number
Reynolds number is a dimensionless quantity that determines the nature of
flow of fluid over a surface.
Reynolds number (Re) = =
2 2
2 2
2 2
2 2
Body Pressure Inertia term Viscous termforce termterm
u u u p u uu v X
t x y x x y
v v v p v vu v Y
t x y y x y
ρ ρ µ
ρ ρ µ
∂ ∂ ∂ ∂ ∂ ∂+ + = − + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂+ + = − + + ∂ ∂ ∂ ∂ ∂ ∂
Inertia forces
Viscous forces
VD VDρµ ν
=
Fluid Mechanics 143
where
ρ = density
µ = dynamic viscosity
v = kinematic viscosity
V = velocity
D = effective diameter
Fig. 6.3 Sources and sinks
Engineers’ Guide to Rotating Equipment144
Fig. 6.4 Flow regimes
Fluid Mechanics 145
Low Reynolds numbers (below about 2000) result in laminar flow.
High Reynolds numbers (above about 2300) result in turbulent flow.
Values of Re for 2000 < Re < 2300 are generally considered to result in
transition flow. Exact flow regimes are difficult to predict in this region.
6.4 Boundary layersFigure 6.5 shows boundary layer velocity profiles for dimensional and non-
dimensional cases. The non-dimensional case is used to allow comparison
between boundary layer profiles of different thickness.
Definitions
• The boundary layer is the region near a surface or wall where the
movement of a fluid flow is governed by frictional resistance.
• The main flow is the region outside the boundary layer that is not
influenced by frictional resistance and can be assumed to be ‘ideal’ fluid
flow.
• Boundary layer thickness. The thickness of the boundary layer is
conventionally taken as the perpendicular distance from the surface of a
component to a point in the flow where the fluid has a velocity equal to
99 per cent of the local mainstream velocity.
Fig. 6.5 Boundary layer velocity profiles
u = velocity parallel to
the surface
y = perpendicular
distance from the
surface
δ = boundary layer
thickness
U1= mainstream velocity
u = velocity parameters
u/U1 (non-
dimensional)
y = distance parameter
y/δ (non-
dimensional)
Dimensional case Non-dimensional case
Engineers’ Guide to Rotating Equipment146
Some boundary layer equations
Boundary layer equations of turbulent flow
6.5 Isentropic flowFor flow in a smooth pipe with no abrupt changes of section:
• Continuity equation
• Equation of momentum conservation
–dp A = (Aρu)du
• Isentropic relationship
p = cρk
• Sonic velocity
These lead to an equation being derived on the basis of mass continuity,
i.e.
or
0p
y
∂ =∂
0u v
x y
∂ ∂+ =∂ ∂
d d d0
u A
u A
ρρ
+ + =
2 d
d
pa
ρ=
2d duM
u
ρρ
= −
2 d duM
u
ρρ
= −
u u pu
x y x y
τρ ∂ ∂ ∂ ∂+ = − + ∂ ∂ ∂ ∂
' 'u
u vy
τ µ ρ∂= −∂
Fluid Mechanics 147
Table 6.4 shows equations relating to convergent and convergent–divergent
nozzle flow.
Table 6.4 Isentropic flows
Pipe flows
Convergent nozzle flows Flow velocity
Flowrate
m = ρuA
Convergent–divergent nozzle flows Area ratio
6.6 Compressible one-dimensional flowBasic equations for 1-D compressible flow are:
Euler’s equation of motion in the steady state along a streamline
or
= constant
so
= constant
where To = total temperature
ρρ
− = 2d duM
u
ρρ
− = − √
1
2 1–1
k
ko
o o
pku
k p
( )
( )
−
−
+ =
+ − −
√
11
1o
1
o
2
1
*1
11
kk
k
k
p
k pA
Apk
k p
21 d d 10
d d 2
pu
s sρ + =
21
2
dpu
ρ+∫
21R
1 2
kT u
k+
−
/( 1) /( 1)
20 0 11
2
k k k kp T kM
p T
− − − = = +
Engineers’ Guide to Rotating Equipment148
6.7 Normal shock waves
One-dimensional flow
A shock wave is a pressure front that travels at speed through a gas. Shock
waves cause an increase in pressure, temperature, density and entropy and a
decrease in normal velocity.
Equations of state and equations of conservation applied to a unit area of
shock wave give (see Fig. 6.6)
State
p1/ρ1T1 = p2/ρ2T2
Mass flow
Momentum
p1 + ρ1u12 = p2 + ρ2u2
2
Energy
1 1 2 2m u uρ ρ= =
2 2
1 2
1 2 2 2
p p p
u uc T c T c T+ = + =
Fig. 6.6 Normal shock waves
p1 p2
ρ1ρ2u1 u
p1ρ1 p2ρ2
u1 u
Fluid Mechanics 149
Pressure and density relationships across the shock are given by the
Rankine–Hugoniot equations
Static pressure ratio across the shock is given by
Temperature ratio across the shock is given by
Velocity ratio across the shock is given from continuity by
u2/u1 = ρ1/ρ2
so
In axisymmetric flow the variables are independent of θ so the continuity
equation can be expressed as
Similarly in terms of stream function ψ
2
2 1
21
1
( 1)1
( 1)
1
1
p
p
γ ργ ργ ργ ρ
+ −−= + −−
( )( )
2
12
21
1
11
1
1
1
p
p
p
p
γγργργ
++
−= + +
−
21 2
2
2 ( 1)
1
p M
p
γ γγ
− −=+
2 2 2
1 1 1
T p
T p
ρρ
=
2 22 1 1
21 1
2 ( 1) 2 ( 1)
1 ( 1)
T M M
T M
γ γ γγ γ
− − + −= + +
22 1
21 1
2 ( 1)
( 1)
u M
u M
γγ
+ −=+
2
2
(sin )1 ( ) 10
sin
RqR q
R RR
ϕϕϕ ϕ
∂∂ + =∂ ∂
2
1
sinRq
R
ψϕϕ
∂=∂
1
sinq
R Rϕ
ψϕ
∂= −∂
Engineers’ Guide to Rotating Equipment150
The pitot tube equation
An important criterion is the Rayleigh supersonic pitot tube equation (see
Fig. 6.7).
Pressure ratio
/( 1)
2
1
02
1/( 1)2
11
1
2
2 ( 1)
1
Mp
p M
γ γ
γ
γ
γ γγ
−
−
+ =
− − +
M1ρ1p1u1 p2
ρ2
M2
p02
Fig. 6.7 Pitot tube
Fluid Mechanics 151
6.8 Axisymmetric flowsAxisymmetric potential flows occur when bodies such as cones and spheres
are aligned into a fluid flow. Figure 6.8 shows the layout of spherical co-
ordinates used to analyse these types of flow.
Fig. 6.8 Axisymmetric flows
Relationships between the velocity components and potential are given by
6.9 Drag coefficientsFigure 6.9 shows drag types and ‘rule of thumb’ coefficient values.
1 1
sinRq q q
R R Rθ ϕ
φ φ φϕ θ ϕ
∂ ∂ ∂= = =∂ ∂ ∂
Engineers’ Guide to Rotating Equipment152
Fig. 6.9 Drag coefficients
α
CHAPTER 7
Centrifugal Pumps
7.1 SymbolsFigure 7.1 shows some typical symbols used in schematic process and
instrumentation diagrams (PIDs) incorporating items of rotating equipment
(including pumps, fans, and compressors).
7.2 Centrifugal pump typesThere are several hundred identifiable types of pump design tailored for
varying volume throughputs and delivery heads, and including many
specialized designs for specific fluid applications. The most common type,
accounting for perhaps 80 per cent of fluid transfer applications, is the broad
‘centrifugal pump’ category.
There is a wide variety of centrifugal pump designs. Figure 7.2 shows
some typical examples.
Figure 7.2(a) shows a back pull-out version of a basic, single-stage,
centrifugal design. This allows the rotor to be removed towards the motor
without disturbing the suction or delivery pipework. This type is commonly
used for pumping of acids or hazardous fluids in the chemical and
petrochemical industry.
Figure 7.2(b) shows a standard, horizontal, multi-stage, centrifugal design
with a balance disc to enable axial thrust to be hydraulically balanced. The
most common application is for high-pressure boiler feed water.
Figure 7.2(c) shows a horizontal, multi-stage, centrifugal pump using the
side-channel principle combined with a radial flow suction stage impeller.
This special impeller, with an axial inlet branch, is arranged upstream of the
open star vane impellers. In this way, combination pumps are obtained
Engin
eers
’G
uid
e to
Rota
ting E
quip
ment
154
Fig. 7.1 Some typical PID symbols (Courtesy MS Visio)
Centrifugal Pumps 155
Fig. 7.2(a) Single-stage, centrifugal pump
(back pull-out design)
Fig. 7.2(b) Horizontal, multi-stage, centrifugal pump
Engineers’ Guide to Rotating Equipment156
Fig. 7.2(c) Side-channel, multi-stage, centrifugal pump
(self-priming with low NPSH inlet stage)
Fig. 7.2(d) Vertical, centrifugal, mixed-flow pump
Centrifugal Pumps 157
Fig. 7.2(e) Vertical barrel, multi-stage, centrifugal pump
which, in addition to the specific features of the side-channel principle, e.g.
self-priming, gas handling capacity, and high head per stage, have a very
low Net Positive Suction Head (NPSH) requirement. Applications include
boiling liquids with low suction heads, condensate, boiler feed water, liquid
gas, and refrigerants.
Figures 7.2(d) and (e) show vertical, multi-stage designs.
Engineers’ Guide to Rotating Equipment158
7.3 Pump performanceThere are many pump performance parameters, some of which are complex
and may be presented in a non-dimensional format.
Volume flowrate q
Flowrate is the first parameter specified by the process designer who bases
the pump requirement on the flowrate that the process needs to function.
This ‘rated’ flowrate is normally expressed in volume terms and is
represented by the symbol q, with units of m3/s.
Head H
Once rated flowrate has been determined, the designer then specifies a total
head H required at this flowrate. This is expressed in metres and represents
the usable mechanical work transmitted to the fluid by the pump.
In general, the usable mechanical energy of a liquid is the sum of energy
of position, pressure energy, and dynamic energy. The pressure energy per
unit of weight of the liquid that is subject to the static pressure p is termed
the ‘pressure head’ p/(ρg). The dynamic energy of the liquid, per unit of
weight, is termed the ‘velocity head’ v2/2g.
The total head H is, therefore, composed of
zd – zs = difference of altitude (i.e. of height) between the outlet
branch and the inlet branch of a pump
= difference of pressure head of the liquid between the outlet
branch and the inlet branch of a pump
= difference of velocity head of the liquid between the outlet
branch and the inlet branch of the pump
From the above, the total head of the pump is
H = (zd – zs) +
Together q and H define the ‘duty point’, the core FFP criterion.
Net Positive Suction Head (NPSH)
NPSH is slightly more difficult to understand. Essentially, it is a measure of
the pump’s ability to avoid cavitation in its inlet (suction) region. This is
done by maintaining a pressure excess above the relevant vapour pressure in
this inlet region. This pressure excess keeps the pressure above that at which
cavitation will occur. Acceptance guarantees specify a maximum NPSH
required. The unit is metres.
d sp p
gρ−
2 2
d s
2
v v
g
−
2 2
d s d s
2
p p v v
g gρ− −+
Centrifugal Pumps 159
The reference plane for the NPSH value is defined by the horizontal plane
that passes through the centre of the circle. This is determined by the most
extreme points of the leading edge of the blades (Fig. 7.3). In the case of
double-entry pumps with a shaft that is not horizontal, the impeller inlet
located at the higher level is the determining factor. For pumps with a
horizontal shaft the reference plane lies in the centre of the shaft. For pumps
with a vertical shaft or a shaft that is inclined to the vertical, the position of
the impeller inlet, and hence the reference plane for the NPSH value, cannot
be determined from the outside and it has to be given by the manufacturer.
Available NPSH of an installation
The available NPSH value (NPSHavail) of an installation (see Fig. 7.4) is the
difference between the total head (static pressure head (ps + pb)/ρg plus
velocity head vs2/2g) and the vapour pressure head pD/ρg referred to the
reference plane for the NPSH value
NPSHavail =
= difference of level between the centre of the inlet branch of
the pump and the reference plane for the NPSH value.
is +ve if the reference plane for the NPSH value lies below the
centre of the pump inlet.
Fig. 7.3 Reference plane for NPSH
2
d b s Ds
2
p p v pz
g g gρ ρ+ ′+ − +
sz′
sz′
Engineers’ Guide to Rotating Equipment160
is –ve if the reference plane for the NPSH value lies above the
centre of the pump inlet (see Fig. 7.3).
is zero if the reference plane for the NPSH value lies at the same
level as the centre of the pump inlet.
The total head at the centre of the inlet connection of the pump can be
derived from the total head at the system inlet.
If a static suction lift Hsgeo = zs – ze has to be taken into account, then
and hence the available NPSH value of the installation is
sz′
sz′
2 2
s b s e b esgeo vs– –
2 2
p p v p p vH H
g g g gρ ρ+ ++ = +
2
e b D eavail sgeo vs sNPSH = – – +
2
p p p vH H z
g gρ+ − ′+
Fig. 7.4 Available NPSH of a system
Centrifugal Pumps 161
or where the pump draws from an open container (pe = 0), i.e. under suction
lift conditions
If a static suction head Hzgeo = –Hsgeo = ze – zs is given, the available NPSH
value of the installation is
or where the pump delivers from an open container (pe = 0), i.e. under
suction head conditions
In practice the velocity head ve2/2g in the container on the suction side of the
pump is small enough to be neglected.
For trouble-free operation of a pump the condition NPSHavail ≥ NPSHreq has
to be satisfied. For reasons of safety and to cover transient conditions, it is
recommended that an excess of approximately 0.5 m is provided, i.e.
NPSHavail ≥ NPSHreq + approx. 0.5 m
Other criteria
• Pump efficiency (η per cent): the efficiency with which the pump
transfers mechanical work to the fluid.
• Power (P) Watts consumed by the pump.
• Noise and vibration characteristics.
It is normal practice for the above criteria to be expressed in the form of
‘acceptance guarantees’ for the pump.
2
b D eavail sgeo vs sNPSH = – – +
2
p p vH H z
g gρ− ′+
2
e b D eavail sgeo vs sNPSH = – +
2
p p p v+ H H z
g gρ+ − ′+
2
b D eavail sgeo vs sNPSH = + – +
2
p p vH H z
g gρ− ′+
Engineers’ Guide to Rotating Equipment162
The q/H curve
The test is carried out at a nominally constant speed, and the head H
decreases as flowrate q increases, giving a negative slope to the curve. Note
how the required ‘duty point’ is represented, and how the required pump
power and efficiency change as flowrate varies.
The NPSH (required) curve
NPSH needs two different sets of axes to describe it fully. The lower curve
in Fig. 7.5 shows how NPSH ‘required’ to maintain full head performance
rises with increasing flowrate. Note, however, that this curve is not obtained
directly from the q/H test; it is made up of three or four points, each point
7.4 Pump characteristicsFigure 7.5 shows a typical centrifugal pump characteristic.
Fig. 7.5 Typical centrifugal pump characteristics
Centrifugal Pumps 163
being obtained from a separate NPSH test at a different constant q. This is
normally carried out after the q/H test. In the NPSH test, the objective is for
the pump to maintain full head performance at an NPSH equal to or less than
a maximum ‘guarantee’ value.
Table 7.1 shows indicative values for a large circulating water pump.
Table 7.1 Typical acceptance guarantee schedule
Rated speed n 740 r/min
Rated flowrate q 0.9 m3/s together, these define
Rated total head H 60 m the ‘duty point’
Rated efficiency 80 per cent at duty point
Absorbed power 660 kW at duty point
NPSH Maximum 6 m at impeller eye for 3 per cent total
head drop
Vibration Vibration measured at the pump bearing shall not
exceed 2.8 mm/s r.m.s. at the duty point
Noise Maximum allowable level = 90 dB(A) at duty point
(at agreed measuring locations)
Now the specification states:
• Tolerances: ± 1.5 per cent on head H and ± 2 per cent on flow q (these are
typical, but can be higher or lower, depending on what the designer
wants) but + 0 on NPSH.
• The acceptance test standard: e.g. ISO 3555. This is important; it tells you
a lot about test conditions and which measurement tolerances to take into
account when you interpret the curves.
7.5 Specifications and standardsSome well-proven centrifugal pump test standards are:
• ISO 2548 (identical to BS 5316 Part 1) is for ‘Class C’ levels of accuracy.
This is the least accurate class and has the largest allowable ‘measurement
tolerances’ which are applied when drawing the test curves, and hence the
largest ‘acceptance’ tolerances on q and H.
• ISO 3555 (identical to BS 5316 Part 2) is for ‘Class B’ levels of accuracy,
with tighter test tolerances than for Class C.
• ISO 5198 (identical to BS 5316 Part 3) is for ‘Class A’ (or ‘precision’)
levels of accuracy. This is the most stringent test with the tightest
tolerances.
Engineers’ Guide to Rotating Equipment164
• DIN 1944 Acceptance tests for centrifugal pumps. This is structured
similarly to BS 5316 and has three accuracy classes, in this case denoted
Class I, II, or III.
• API 610 Centrifugal pumps for general refinery service. This is a more
general design-based standard.
• ISO 1940/1 (identical to BS 6861 Part 1) is commonly used to define
dynamic balance levels for pump impellers.
• VDI 2056 is commonly used to define bearing housing or pump casing
vibration. A more complex method, measuring shaft vibration, is covered
by ISO 7919-1 (similar to BS 6749 Part 1).
• DIN 1952 and VDI 2040 are currently withdrawn standards but are still
in common use to specify methods of flowrate q measurement.
7.6 Test procedures and techniquesFigure 7.6 shows a basic centrifugal pump test circuit. The test is carried out
as follows:
Step 1. The q/H test
The first set of measurements is taken at duty point (100 per cent q). The
valve is opened to give a flowrate greater than the duty flow (normally 120
or 130 per cent q) and further readings taken. The valve is then closed in a
series of steps, progressively decreasing the flow (note that we are moving
from right to left on the q/h characteristic). With some pumps, the final
reading can be taken with the valve closed, i.e. the q = 0, ‘shut-off
condition’. The procedure is now: (Fig. 7.7)
• draw in the test points on the q/H axes;
• using the measurement accuracy levels given for the class of pump, draw
in the q/H measured band;
• add the rectangle, which describes the tolerances allowed by the
acceptance guarantee on total head H and flowrate q; ISO 3555 indicates
tolerances of ± 2 per cent H and ± 4 per cent q;
• if the q/H band intersects or touches the rectangle then the guarantee has
been met; note that the rectangle does not have to lie fully within the q/H
band to be acceptable.
It is not uncommon to find different interpretations placed on the way in
which ISO 3555 specifies ‘acceptance’ tolerances. The standard clearly
specifies measurement accuracy levels ± 2 per cent q, ± 1.5 per cent H, but
later incorporates these into a rigorous method of verifying whether the test
curve meets the guarantee by using the formula for an ellipse (effectively
allowing an elliptical tolerance ‘envelope’ around each measured point),
specifying values of 2 per cent H and 4 per cent q to be used as the major
axes lengths of the ellipse.
Centrifugal Pumps 165
Step 2. The efficiency test
The efficiency guarantee is checked using the same set of test measurements
as the q/H test. Pump efficiency is shown plotted against q as in Fig. 7.5. In
most cases, the efficiency guarantee will be specified at the rated flowrate (q).
Step 3. Noise and vibration measurements
Vibration levels for pumps are normally specified at the duty (100 per cent
q) point. The most common method of assessment is to measure the
vibration level at the bearing housings using the methodology proposed by
Fig. 7.6 Centrifugal pump test circuit
Engineers’ Guide to Rotating Equipment166
VDI 2056. This approximates vibration at multiple frequencies to a single
velocity (r.m.s.) reading. It is common for pumps to be specified to comply
with VDI 2056 group T vibration levels, so a level of up to around 2.8 mm/s
is acceptable. Some manufacturers scan individual vibration frequencies,
normally multiples of the rotational frequency, to gain a better picture of
vibration performance.
Pump noise is also measured at the duty point. It is commonly specified
as an ‘A-weighted sound pressure level’ measured in dB(A) at the standard
distance of 1 m from the pump surface.
Step 4. The NPSH test
These are two common ways of doing the NPSH test.
1. One can simply check that the pump performance is not impaired by
cavitation at the specified q/H duty with the ‘installed’ NPSH of the test
rig. This is a simple go/no-go test, applicable only for values of specified
NPSH that can be built in to the test rig. It does not give an indication of
any NPSH margin that exists, hence is of limited accuracy.
Fig. 7.7 Compliance with the q/H guarantee
Centrifugal Pumps 167
2. A comprehensive test technique is to explore NPSH performance more
fully by varying the NPSH over a range and watching the effects. The most
common method is the ‘3 per cent head drop’ method shown in Fig. 7.8.
The test rig suction pressure control circuit is switched in, see Fig. 7.6,
and the suction pressure reduced in a series of steps. For each step, the pump
outlet valve is adjusted to keep the flowrate q at a constant value. The final
reading is taken at the point where the pump head has decayed by at least 3
per cent. This shows that a detrimental level of cavitation is occurring and
defines the attained NPSH value, as shown in Fig. 7.8. In order to be
acceptable, this reading must be less than, or equal to, the maximum
guarantee value specified. Strictly, unless specified otherwise, there is no
‘acceptance’ tolerance on NPSH, although note that ISO 3555 gives a
measurement tolerance of ± 3 per cent or 0.15 m NPSH.
Fig. 7.8 Measuring NPSH – the 3 per cent head drop method
Engineers’ Guide to Rotating Equipment168
Corrections
Correction factors (applied to q, H, P, and NPSH) need to be used if the test
speed of the pump does do not match the rated speed. They are:
• flow q (corrected) = q (measured) × (nsp/n)
• head H (corrected) = H (measured) × (nsp/n)2
• power P (corrected) = P (measured) × (nsp/n)3
• NPSH (corrected) = NPSH (measured) × (nsp/n)2
n = speed during the test
nsp = rated speed
Table 7.2 shows some common practical problems and solutions that arise
from centrifugal pump tests.
Table 7.2 Common problems in pump tests
Problems
The q/H characteristic is above and
to the right of the guarantee point (i.e.
too high).
The q/H characteristic is ‘too low’ –
the pump does not fulfil its guarantee
requirement for q or H.
NPSH is well above the acceptance
guarantee requirements.
Corrective action
For radial and mixed-flow designs,
this is rectified by trimming the
impeller(s). The q/H curve is moved
down and to the left.
Often, up to 5% head increase can be
achieved by fitting a larger diameter
impeller. If this does not rectify the
situation there is a hydraulic design
fault, probably requiring a revised
impeller design. Interim solutions can
sometimes be achieved by:
• installing flow-control or pre-rotation
devices;
• installing upstream throttles.
This is most likely a design problem;
the only real solution is to redesign.
Centrifugal Pumps 169
Excessive vibration over the speed
range.
Excessive vibration at rated speed.
Noise levels above the acceptance
guarantee levels.
7.7 Pump specific speed ns
Specific speed is a dimensionless characteristic relating to the shape of a
pump impeller. In formal terms, it relates to the rotational speed of an
impeller which provides a total head of 1 m at a volumetric flow rate of
1 m3/s. From dynamic similarity, it can be shown that
ns = n .
where
n is in r/min
q is in m3/s
H is in m
The pump must be disassembled.
First check the impeller dynamic
balance using ISO 2373/BS 4999
part 142/IEC.42 or ISO 1940 for
guidance.
Check all the pump components for
‘marring’ and burrs: these are prime
causes of inaccurate assembly. During
re-assembly, check concentricities by
measuring Total Indicated Runout
(TIR) with a dial gauge.
Check the manufacturer’s critical
speed calculations. The first critical
speed should be a minimum 15–20%
above the rated speed.
High vibration levels at discrete,
rotational frequency is a cause for
concern. A random vibration signature
is more likely to be due to the effects
of fluid turbulence.
Pump noise is difficult to measure
because it is masked by fluid flow
noise from the test rig. If high noise
levels are accompanied by vibration a
stripdown and retest is necessary.
1/ 2
s
3 / 4
s
( / )
( / )
q q
H H
Table 7.2 Cont.
Hence substituting qs = 1 and Hs = 1 gives
ns = n .
where q and H refer to the point of optimum efficiency of the impeller.
This formula can be expressed as a characteristic type number so that it
remains non-dimensional, whatever system of units is used. Figure 7.9
shows some approximate design ranges for pump types based on their
specific speed. Figure 7.10 shows the influences of specific speed on the
shape of pump characteristic curves.
Engineers’ Guide to Rotating Equipment170
1/ 2
3 / 4
q
H
Fig. 7.9 Efficiency-specific speed-impeller types –
approximate relationships
Centrifugal Pumps 171
ns = ns = ns = ns =
Fig. 7.10 The influence of specific speed on pump
characteristic shape
Engineers’ Guide to Rotating Equipment172
7.8 Pump balancingTechnically, the balancing of pumps follows the same principles and
standards used for other rotating equipment. However, there are a few points
which are specific to pumps.
The rigid rotor assumption
Except in very unusual design circumstances, pumps are assumed to have
rotors which behave as a rigid body, hence the standard ISO 1940 can be
used. This applies both to pump designs in which the impeller is mounted
between bearings and to those in which the impeller is overhung from a
single bearing.
Static versus dynamic balancing
Rotating equipment can be balanced using either the ‘static’ method, which
uses a single balancing correction plane, or by ‘dynamic’ balancing using
two correction planes and taking into account the resulting couple
imbalance that occurs. Pumps divide neatly into two categories based on the
approximate ratio of the dimensions of the rotating parts.
• Narrow ‘high ratio’ impellers. If the diameter: width ratio of a pump’s
impeller is greater than six, then it is normal to use a simple static
balancing technique, so balance correction is only carried out in one
plane. There is a practical as well as a theoretical angle to this; it can be
difficult to remove sufficient metal from a high ratio impeller without
weakening the impeller itself.
• Low ratio impellers. When the impeller ratio is six or less, then two-plane
dynamic balancing is used. This involves two separate allowable
unbalance limits: one for static unbalance and one for dynamic unbalance,
which takes account of the couple.
Impeller only versus assembly balance
Most pumps’ impellers are balanced alone on the balancing machine, but
there are occasions where the impeller and its rotating shaft are balanced in
their assembled state. The rationale behind this approach is that the specified
balance grade cannot be reached for the separate rotating components – but
it is possible when they are assembled together.
Balance quality grade
European practice is to use ISO 1940 as the basis of specifying pump
balance levels. Unfortunately the standard is not absolutely definitive in
specifying acceptable levels of unbalance for pumps with various rotational
Centrifugal Pumps 173
speeds. Table 1 of the standard indicates an acceptance grade of G6.3 for
pump impellers, but you can consider this as general guidance only – it is
not necessarily applicable to all types of pump. Several major pump
manufacturers use their own acceptance criteria based on a broad fitness-
for-purpose assessment, but these may be changed to fit in with purchasers’
specific requirements. These grades depend on rated speed – slow-speed
pumps such as those for seawater circulation duties run at low speed and so
can tolerate greater unbalance without suffering excessive stresses and
resultant mechanical damage.
7.9 Balance calculationsThe essence of balance calculations is incorporated in Table 1 of ISO 1940.
This can be tricky to follow and it is difficult to obtain accurate readings
from the logarithmic scales. A simpler method using calculation is shown in
Fig. 7.11. The two main criteria are the allowable static residual unbalance
Us and the allowable couple unbalance Uc, which is itself a function of Us
and the physical dimensions of the pump. Figure 7.12 shows a typical
calculation for a supported-bearing rotor balanced alone, i.e. without its
shaft assembly.
The accuracy of balancing results, while important, is rarely a major issue
when witnessing pump balancing tests in the works. The difference in
allowable unbalance between grade G6.3 and G40 for instance is a factor of
six or more, so small errors in balancing accuracy up to about ± 5 per cent
can be treated as second order.
Test speed
There are no hard and fast rules about the test speed to be used during the
balancing test. Theoretically, any speed up to the rated speed could be used,
and give comparable unbalance readings, but practically the minimum
acceptable test speed is governed by the sensitivity of the balancing
machine. If the test speed is too low the machine will not give accurate
results. The type of mandrel used to mount the impeller also has an effect on
the test speed. Mandrels can be of either the fixed collar type, which fits
accurately the impeller bore, or the ‘expanding’ type, which provides a
universal fitting. Expanding mandrels cannot provide such good concentric
accuracy and so can induce errors into the readings.
Mandrel accuracy
Whether a fixed collar or expanding mandrel is used, it must itself be
balanced so that it does not induce errors into the readings of impeller
Engineers’ Guide to Rotating Equipment174
Fig. 7.11 Pump impeller balancing
Centrifugal Pumps 175
Fig. 7.12 Pump rotor balancing
Engineers’ Guide to Rotating Equipment176
unbalance. The acceptable balance grade for mandrels is normally taken as
ISO 1940 G2.5, but in a practical works situation it is acceptable to use an
approximate method, by measuring concentricities. This gives a first-order
approximation of the mandrel balance grade – good enough for most
purposes. Note how the typical acceptable concentricity limit (TIR)
decreases as the pump rated speed increases.
Pump rated speed (r/min) Mandrel accuracy (TIR)
Up to 1500 45 µm
1500–6000 20 µm
6000–7500 10 µm
above 7500 Mandrel not used
Note that expanding mandrels are not used for impellers with rated speeds
above 1500 r/min.
Achieving impeller balance grade
Once the initial unbalance readings have been taken, the impeller (or the
impeller/shaft assembly) has to be balanced so that it meets the specified
grade. With small pump impellers (up to about 250 mm diameter) this is
done by removing metal either by machining or hand grinding. For larger
designs, and in particular impellers with a depth:diameter ratio of more than
1:2, it is practical to add balancing weights. In these sizes it is common for
the impeller to be dynamically balanced using two correction planes. Figure
7.11 shows a typical example of a seawater pump impeller in which balance
is achieved using a combination of the two methods. Accurately weighted
bars are welded into the nose cone of the impeller while material is
machined off the inside of the hub end by mounting the impeller ‘off centre’
in a vertical jig boring machine. There is often a limit on how much metal
can be removed – a maximum 25 per cent of the impeller shroud ring wall
thickness (which is where the metal is normally removed from) is a good
rule of thumb.
7.10 Pump components – clearances and fitsThe correct clearances and fits are a basic but important part of a pump’s
fitness for purpose. The importance of obtaining the accurate dimensions,
particularly on bore diameters, increases with pump size. Figure 7.13 shows
Centrifugal Pumps 177
typical categories of fit used for a vertical cooling water pump. These are
chosen from the common mid-range toleranced fits given in ISO R286.
Expect to see (as a guideline), the following categories:
• Bearing to shaft sleeve – running clearance fit
• Impeller to shaft – transition fit better than H7/k6
• Casing wear-ring to casing – locational interference fit
• Impeller to casing wear-ring – running clearance fit
• Casing section joints – transition ‘spigot’ fit (for tight loca-
tion rather than accuracy)
• Shaft ‘muff’ couplings – ‘sliding’ clearance fit, e.g. H7/g6
• Bearing housing to bearing – locational clearance fit, e.g. H7/h6
Fig. 7.13 Pump assembly checks
Engineers’ Guide to Rotating Equipment178
Table 7.3 shows some of the wide range of technical standards relevant to
centrifugal pumps.
Table 7.3 Technical standards – centrifugal pumps
Standard Title Status
BS 5257: 1975 Specification for horizontal end-
suction centrifugal pumps (16 bar).
Current
BS 5316-1: 1976,
ISO 2548-1973
Specification. Acceptance tests for
centrifugal, mixed-flow, and axial
pumps. Class C tests.
Current
BS 5316-2: 1977,
ISO 3555-1977
Specification for acceptance tests for
centrifugal, mixed-flow, and axial
pumps. Class B tests.
Current
BS ISO 3069: 2000 End-suction centrifugal pumps.
Dimensions of cavities for mechanical
seals and for soft packing.
Current
BS EN ISO 5198: 1999 Centrifugal, mixed-flow, and axial
pumps. Code for hydraulic
performance tests. Precision class.
Current
BS EN ISO 9905: 1998 Technical specifications for centrifugal
pumps. Class I.
Current
BS EN ISO 9906: 2000 Rotodynamic pumps. Hydraulic
performance acceptance tests.
Grades 1 and 2.
Current
BS EN ISO 9908: 1998 Technical specifications for centrifugal
pumps. Class III.
Current
BS EN 733: 1995 End-suction centrifugal pumps, rating
with 10 bar with bearing bracket.
Nominal duty point, main dimensions,
designation system.
Current
BS EN 735: 1995 Overall dimensions of rotodynamic
pumps. Tolerances.
Current
BS EN 1151: 1999 Pumps. Rotodynamic pumps.
Circulation pumps having an electrical
effect not exceeding 200 W for
heating installations and domestic hot
water installations. Requirements,
testing, marking.
Current
BS EN 22858: 1993,
ISO 2858: 1975
End-suction centrifugal pumps (rating
16 bar). Designation, nominal duty
point, and dimensions.
Current
Centrifugal Pumps 179
BS EN 23661: 1993,
ISO 3661: 1977
End-suction centrifugal pumps.
Baseplate and installation dimensions.
Current
BS EN 25199: 1992,
ISO 5199-1986
Technical specifications for centrifugal
pumps. Class II.
Current, work
in hand
93/303211 DC Firefighting pumps. Part 1.
Requirements for firefighting
centrifugal pumps with primer (prEN
1028-1).
Current, draft
for public
comment
93/303212 DC Firefighting pumps. Part 2. Testing of
firefighting centrifugal pumps with
primer (prEN 1028-2).
Current, draft
for public
comment
Table 7.3 Cont.
CHAPTER 8
Compressors and Turbocompressors
8.1 CompressorsCompressor designs vary from those providing low-pressure delivery of a
few bars up to very high-pressure applications of 300 bars. The process fluid
for general industrial use is frequently air, while for some specialized
process plant applications it may be gas or vapour. There are several basic
compressor types, the main difference being the way in which the fluid is
compressed. These are:
• Reciprocating compressors The most common positive displacement type
for low-pressure service air. A special type with oil-free delivery is used
for instrument air and similar critical applications.
• Screw compressors A high-speed, more precision design used for high
volumes and pressures and accurate variable delivery.
• Rotary and turbocompressors High-volume, lower-pressure applications.
These are of the dynamic displacement type and consist of rotors with
vanes or meshing elements operating in a casing.
Other design types are: lobe-type (Rootes blowers), low-pressure
exhausters, vacuum pumps, and various types of low-pressure fans.
Compressor performance
The main fitness-for-purpose (FFP) criterion for a compressor is its ability
to deliver a specified flowrate of air or gas at the pressure required by the
process system. Secondary FFP criteria are those aspects that make for
correct running of the compressor; the most important one, particularly for
reciprocating designs, is vibration.
Engineers’ Guide to Rotating Equipment182
The main performance-related definitions are listed in ISO 1217. They are:
• Total pressure p Total pressure is pressure measured at the stagnation
point, i.e. there is a velocity effect added when the gas stream is brought
to rest. In a test circuit, ‘absolute total pressure’ is measured at the
compressor suction and discharge points for use in the calculations.
• Volume flowrate q There are three main ways of expressing this (see Fig. 8.1).
• Free air delivery q (FAD) This is the volume flowrate measured at
compressor discharge and referred to free air (the same as atmospheric
conditions). It is the definition nearly always quoted in compressor
acceptance guarantees.
• Actual flowrate This is the volume flowrate, also measured at compressor
discharge, but referred specifically to those conditions (these are total
measurements) existing at the compressor inlet during the test.
• Standard flowrate This is nearly the same as FAD. It is the volume
flowrate, measured at the discharge, but referred to a standard set of inlet
conditions. A common set of standard conditions is 1.013 bar and 0 °C
(273 K). A correction factor is needed to convert to FAD.
• Specific energy requirement This is the shaft input power required per unit
of compressor volume flowrate. Power is normally an acceptance
guarantee parameter.
Fig. 8.1 Three ways of expressing compressor flowrate
Compressors and Turbocompressors 183
Compressor acceptance testing
The overall objective of a compressor acceptance test is to check
compliance with the specified performance guarantees, which will look
something like this:
• specified inlet pressure p1 and inlet temperature T1; note that these are
often left implicit, perhaps being described as ‘ambient’ conditions;
• required FAD capacity q at delivery pressure p2;
• power consumption P at full load;
• vibration – normally specified for compressors as a velocity (using VDI
2056);
• noise – expressed as an ‘A-weighted’ measurement in dB(A).
Test circuits
There are several possible layouts of test circuits. The most common type
for air applications is the ‘open’ circuit, i.e. the suction is open to
atmosphere, which is representative of the way that the compressor will
operate when in service. If an above-atmospheric suction pressure is
required then the test circuit will be a closed loop.
The flowrate (FAD) can be measured using an orifice plate flow meter on
either the suction or discharge side of the compressor. Typically, it is
measured on the discharge side, with a receiver vessel interposed between
the orifice and the compressor discharge (see Fig. 8.2).
The test
The performance test itself consists of the following steps:
• circuit checks;
• run the compressor until the system attains steady state conditions (up to
4 h);
• check the system parameters comply with allowable variations as in ISO
1217;
• make minor adjustments as necessary, but only those essential to maintain
the planned test conditions;
• take readings at regular intervals (say 15 min) over a period of 2–4 h with
the compressor running at full load;
• check again for obvious systematic errors in the recorded parameters;
• carry out functional checks of unloading equipment, relief valves, trips,
and interlocks;
• perform the noise and vibration measurements;
• do the performance calculations and compare the results with the
guarantee requirements (see Table 8.1).
Engineers’ Guide to Rotating Equipment184
Fig. 8.2 Compressor test circuit
Compressors and Turbocompressors 185
Calculate q (FAD)
by
q(FAD) = √1 2
1
kT h.p
p T
This q(FAD) will be in l/s.
Convert to m2/h using
m2/h = 1/s × 3.6
Do you need any
conversion factors?
If the test speed is different
from the rated speed,
correct the q(FAD) by
q(FAD) (corrected) =
q)FAD)(test) ×
Compare it with the q(FAD)
requirements of the
guarantee
Check power consumption
kW
Any correction if necessary
Power (corrected) =
Power (test) ×
If specifically required by
the guarantee express
power consumption in
‘specific energy’ terms by:
Specific energy =
rated speed
test speed
rated speed
test speed
energy consumption
q(FAD)
Where
q = Volume flowrate
h = Pressure drop across nozzle
(mmH20)
K = Nozzle constant (remember the
check described earlier)
T1 = Temperature (absolute K) at
compressor inlet
T = Temperature (absolute K)
downstream of the nozzle
p1 = Pressure (absolute mmHg) at
compressor inlet
p2 = Pressure (absolute mmHg)
downstream of the nozzle
Absolute pressure – gauge reading +
atmospheric pressure (check the
barometer)
There is an allowable tolerance of ± 4–6%
at full load depending on the size of
compressor – check with BS 1574 if in
doubt
Normally measured using two wattmeters
Watch the units: a normal unit is kW h/l
THEN
REMEMBER
REMEMBER
Step 5
Step 4
Step 3
NEXT
Step 2
Step 1
This simplified correction is normally the
only one you will need for a test under
BS 1571 Part 2
Table 8.1 Evaluation of performance test results
Engineers’ Guide to Rotating Equipment186
Compressor specifications and standards
The most commonly used test standard is:
• ISO 1217: 1986 Methods for acceptance testing (identical to BS 1571
Part 1).
This gives comprehensive testing specifications and arrangements for the
major compressor types. It is particularly suitable for testing an unproven or
‘special’ compressor design.
Other relevant standards are shown in Table 8.2.
Table 8.2 Technical standards – compressors
Standard Title Status
BS 1553-3: 1950 Graphical symbols for general
engineering. Graphical symbols for
compressing plant.
Current
BS 1571-2: 1975 Specification for testing of positive
displacement compressors and
exhausters. Methods for simplified
acceptance testing for air
compressors and exhausters.
Current,
confirmed
BS 1586: 1982 Methods for performance testing and
presentation of performance data for
refrigerant condensing units.
Current
BS 1608: 1990 Specification for electrically driven
refrigerant condensing units.
Current
BS 3122-1: 1990,
ISO 917: 1989
Refrigerant compressors. Methods of
test for performance.
Current
BS 6244: 1982,
ISO 5388-1981
Code of practice for stationary air
compressors.
Current
BS 7316: 1990 Specification for design and
construction of screw and related
type compressors for the process
industry.
Current,
proposed for
withdrawal
BS 7321: 1990,
ISO 8011: 1988
Specification for design and
construction of turbo-type
compressors for the process industry.
Current,
proposed for
withdrawal
BS 7322: 1990,
ISO 8012: 1988
Specification for design and
construction of reciprocating-type
compressors for the process industry.
Current,
proposed for
withdrawal
Compressors and Turbocompressors 187
BS 7854-3: 1998,
ISO 10816-3: 1998
Mechanical vibration. Evaluation of
machine vibration by measurements
on non-rotating parts. Industrial
machines with nominal power above
15 kW and nominal speeds between
120 r/min and 15 000 r/min when
measured in situ.
Current
BS ISO 1217: 1996 Displacement compressors.
Acceptance tests.
Current
BS EN 255-1: 1997 Air conditioners, liquid chilling
packages, and heat pumps with
electrically driven compressors.
Heating mode. Terms, definitions,
and designations.
Current
BS EN 1012-1: 1997 Compressors and vacuum pumps.
Safety requirements. Compressors.
Current
BS EN 1012-2: 1997 Compressors and vacuum pumps.
Safety requirements. Vacuum pumps.
Current
BS EN 12583: 2000 Gas supply systems. Compressor
stations. Functional requirements.
Current
BS EN 12900: 1999 Refrigerant compressors. Rating
conditions, tolerances and
presentation of manufacturer's
performance data.
Current
95/710815 DC Measurement of noise emission from
compressors and vacuum pumps
(engineering method) (prEN 12076).
Current, draft
for public
comment
95/715797 DC Petroleum and natural gas industries.
Rotary-type positive displacement
compressors. Part 2. Packaged air
compressors. (Joint TC 118-TC
67/SC 6) (ISO/DIS 10440-2.)
Current, draft
for public
comment
95/715798 DC Petroleum and natural gas industries.
Rotary-type positive displacement
compressors. Part 1. Process
compressors. (Joint TC 188/TC
67/SC 6) (ISO/DIS 10440-1.)
Current, draft
for public
comment
96/702049 DC prEN ISO 917. Testing of refrigerant
compressors.
Current, draft
for public
comment
96/702050 DC prEN ISO 9309. Refrigerant
compressors. Presentation of
performance data.
Current, draft
for public
comment
Table 8.2 Cont.
Engineers’ Guide to Rotating Equipment188
8.2 TurbocompressorsFor very large volume throughputs of gas (generally air) at low pressure, a
centrifugal dynamic displacement machine is used, known generically as a
‘turbocompressor’. Turbocompressors may have single or multiple pressure
stages, depending on the delivery pressure and volume required. Although
they work using the same thermodynamic and fluid mechanics ‘rules’ as
reciprocating or screw compressors, they are very different mechanically,
the main reason being because of their high rotational speed.
Turbocompressors are fast and potentially dangerous machines – a typical
300–600 kW machine can have rotational speed of up to 25 000 r/min,
giving impeller tip speeds of around 500 m/s. Typical uses are for large-
scale ventilation of enclosed spaces and for aeration of fluid-bed based
chemical processes such as gas desulphurization or effluent treatment plant.
96/706683 DC Reciprocating compressors for the
petroleum and natural gas industries
(ISO/DIS 13707).
Current, draft
for public
comment
96/708979 DC Centrifugal compressors for general
refinery service in the petroleum and
natural gas industries (ISO/DIS
10439).
Current, draft
for public
comment
96/716066 DC Petroleum and natural gas industries.
Packaged, integrally geared
centrifugal air compressors for
general refinery service (ISO/DIS
10442).
Current, draft
for public
comment
97/700630 DC Refrigerating systems and heat
pumps. Safety and environmental
requirements. Refrigerant
compressors (prEN 12693).
Current, draft
for public
comment
99/716305 DC prEN 13771-1. Refrigerant
compressors and condensing units
for refrigeration. Performance testing
and test methods. Part 1. Refrigerant
compressors.
Current, draft
for public
comment
00/706276 DC ISO/DIS 5389. Turbocompressors.
Performance test code.
Current, draft
for public
comment
BS 1571: Part 1:
1975,
ISO 1217-1974
Specification for testing of positive
displacement compressors and
exhausters. Acceptance tests.
Withdrawn,
revised
Table 8.2 Cont.
Compressors and Turbocompressors 189
Performance and guarantees
Turbocompressor guarantees are based on the typical performance
characteristic shape shown in Fig. 8.3. This consists of a series of operating
curves (representing different vane settings) plotted within a set of
pressure–volume axes. There is an upper operating limit at the top of the
pressure range. The machine will not operate properly above this point,
known as the ‘surge line’. The characteristic shown is typical for a
single-stage turbocompressor – the range and gradients will be different
for a multi-stage machine. Another guarantee criterion is noise.
Turbocompressors are noisy machines: a large unit of 600 kW with a
500 m/s vane tip speed will produce in excess of 98 dB(A). This is above the
safety level for human hearing, so most turbocompressors are fitted with an
acoustic enclosure.
Fig. 8.3 Turbocompressor – the basic performance
characteristic
Mechanical arrangement
Figure 8.4 shows the general mechanical arrangement of a single-stage
turbocompressor. The mechanical design features that differ from those
found on a standard air compressor are:
Engineers’ Guide to Rotating Equipment190
• a step-up gearbox;
• tilting pad thrust bearings;
• inlet guide vanes (IGVs) and/or variable diffuser vanes (VDVs);
• highly rated bearings (100–300 000 h rated life);
• axial alignment of gear wheels accurate to about 10 µm;
• back-up lubricating oil system;
• precision ‘Hirth toothed’ shaft coupling.
The turbocompressor casings can be fabricated or cast. Special sprung
resilient mountings are used to minimize the transmission of structural
vibration.
The fluid characteristics of turbocompressors work on the same concept
as other rotodynamic machinery: the principle of changing dynamic energy
into static energy, i.e speed is ‘converted’ into pressure. Downstream
diffusers and the specially shaped spiral casing are used to help optimize the
flow regime. Air delivery pressure is limited by the position of the surge line
on the characteristic, so guarantees are normally quoted in terms of a
delivery pressure in ‘water gauge’ (metres of H2O) at a rated continuous
volume throughput.
Compared to other compressor types, the delivery pressure is low,
normally a few bars. The absolute maximum for centrifugal machines is 18
bar, although few practical machines go this high, except for perhaps sparge-
air applications in some specialist chemical processes. Inlet air conditions
are quoted as an absolute temperature and pressure, with the addition
of relative humidity. This makes the performance calculations for
turbocompressors more complicated than the simplified free air delivery
(FAD) method used for normal compressors, so specialist technical
standards are needed. Both single- and multi-stage machines are specified
with a minimum ‘turndown’ ratio (normally 40–60 per cent) set by the
process system that the turbocompressor supplies. Machine efficiencies are
high – near 90 per cent.
Specifications and standards
There are at least three different sets of standards in common use: VDI and
BS of European origin and the ASME PTC from the USA. They use similar
principles and methodologies, although differing slightly in some areas of
detail.
Com
pre
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191
Split gearbox casing Oil pump drive gears
Oil pump
Gear wheel
Ball bearings
(300 000 hrs
bio life)
Motor drive
Tilting-pad
thrust bearing
Gear pinionDischarge casing
Inlet
casing
Impeller
(single stage)
Diffuser guide vanes (DGVs)
Fig. 8.4 Single-stage turbocompressor – general mechanical arrangement
Engineers’ Guide to Rotating Equipment192
Acceptance and performance tests
VDI 2045 (Table 8.3) is the most comprehensive technical standard
available on the subject of turbocompressor performance tests. VDI 2045 is
unlike the comparable BS or ASME PTC standard in that it relates to both
turbocompressors and positive displacement compressors. There are no
significant technical contradictions raised by this approach; it just means
that the standard contains some duplication of sections, to cater for the two
different machine types. Table 8.3 is a guide to finding the most important
pieces of information in the standard.
Part 1 concentrates on guarantee testing and the principles of the
conversion and comparison of test results. Important parts are:
• Emphasis on performance guarantees: it concentrates on the three main
guarantee parameters: fluid volume throughput, discharge pressure, and
power consumption.
• Measurement uncertainties: the same philosophy of measurement
uncertainties and errors is used as in the standard for pump testing, ISO
3555. Each measured parameter is given a level of accuracy, depending
on the instrument or technique used, and these accumulate into an overall
uncertainty level. (It can also be thought of as a confidence level that
applies to the test results.) The standard itemizes these uncertainties, and
suggests suitable percentage values to use.
• Test deviations: these are the amounts by which the various measured
parameters are allowed to deviate during a performance test and still be
considered acceptable readings. The standard gives recommended levels.
• Referenced standards: one of the strong points of VDI 2045 is the clear
way it cross-references other related standards that apply to the test. Most
of these are to do with the hardware and layout of the test rig.
ASME PTC-10 is the most common code used in the USA and in the
offshore and process industries. As with the other standards, it concentrates
on performance aspects rather than the mechanics of turbocompressor
machines. The unique thing about PTC-10 is that it caters for three classes
of turbocompressor tests. Class I is used when the test gas and arrangement
are the same as the machine will see in service. Class II and III involve a
degree of performance prediction, i.e. where the test gas is different,
normally for reasons of safety. Turbocompressors for explosive gas service
are normally tested on air, under the provisions of PTC-10 Class II or III.
The difference between Class II and III is only in the way of processing the
test results, depending on the level of ‘real gas’ assumptions that are used
during the calculations. Table 8.4 shows other standards referenced by PTC-
10.
Compressors and Turbocompressors 193
An old, well-established standard dedicated to turbocompressors is BS
2009. Sections 1 and 2, which are short, cover temperature and pressure
measurement techniques and symbols. Section 3 is about the correction of
acceptance test results to guarantee conditions. There are no separate test
classes, as in PTC-10. Diagrams of acceptable test layouts are shown in the
appendix of the standard.
Table 8.3 Important information in VDI 2045
VDI 2045: 1993: Acceptance and performance tests on
turbocompressors and displacement compressors
Part 1: Test procedure and comparison with guaranteed values
Part 2: Theory and examples
Referenced standards
• VDI 2045 Suction line inlet diaphragm
• DIN 1952
• VDI 2059: Part 3 Shaft vibration of industrial turbosets – measurement
and evaluation
• VDI 2056 Criteria for assessing mechanical vibration of machines. This
standard deals with ‘housing’ vibration and is similar to ISO 2372/BS
4675
BS 2009: Code for acceptance tests for turbo-type compressors and
exhausters
Referenced standards
• BS 1571: Part 2: 1984 Method for simplified acceptance testing for air
compressors and exhausters. This replaces BS 726
• BS 1042: Part 1 (various sections): Pressure differential devices
• BS 848: Part 1: 1980 Fans for general purposes – methods of testing
performance
VDI 2045 Part 1
Subject Section
The objective of guarantees 1.3.3
‘Type test’ acceptance 1.3.6
List of symbols and indices 2
The principle of measurement uncertainty 3.1.1
Important measurement guidelines (cross-references) 3.1.2
Fluid volumetric/mass flow guidelines 3.7.1
Power measurement 3.9.2
Energy balance assumptions 3.9.4
Engineers’ Guide to Rotating Equipment194
Performance test : preparation 4.1
: general requirements 4.2
: allowable deviations 4.2.2 and 5.3.
Tables 5 and 6
Measurement uncertainties (test results) 4.4
Conversion of test results to guarantee conditions 5.3, Figs 3 and 7,
Table 5
Typical performance curves 5.3.5, 6.1, 6.2.2.2,
6.2.3, 6.2.4
Testing reporting and documentation requirements 7
VDI 2045 Part 2
Subject Section
Reference boundaries 2.3 and Fig. 3
Performance curves 2.9.1
Guide vane and surge effects 2.9.1
Specimen test results 3.3.2
Conversion to guarantee conditions 3.3.1
Table 8.4 Turbocompressors – ASME PTC-10 referenced
standards
ASME PTC-10: 1986: Compressors and exhausters
Referenced standards
• PTC-1 General instructions
• PTC-19.3 Instruments for temperature measurements
• PTC-19.5 Flow measurement
• PTC-19.3 Measurement of rotational speed
• PTC-19.7 Measurement of power
• ASA 50.4 Motor efficiency measurement IEEE
• PTC-19.6 Electrical measurement in power circuits
• PTC-19.5 Flow coefficients for orifices
Table 8.3 Cont.
Compressors and Turbocompressors 195
Vibration measurement
An important standard is VDI 2059. It is relevant for several types of
turbomachinery, but its principal use is for turbocompressors, mainly
because of their higher speed – up to 30 000 r/min, compared to a practical
maximum of 5000–6000 for other types of turbomachinery. VDI 2059 relies
on four fundamental principles.
• VDI 2059 is about vibration of the shaft relative to its journal bearings.
This is unrelated to the simpler types of ‘housing’ vibration covered by
VDI 2056/BS 4675/ISO 2372.
• Vibration is sensed by non-contacting probes which look at highly
polished areas of the shaft. They are located in two perpendicular (x and
y) planes.
• The measured parameter is shaft displacements measured in microns, not
velocity as used for ‘housing’ vibration. There are two aspects to this: the
absolute level of shaft displacement measurement during a test run, and
the amount by which the displacement changes as the test progresses.
These are referred to by the standard as criterion I and II, respectively.
• The concept of VDI 2059 shaft vibration is that it is not sinusoidal, or in any
way sine-related. This means that it is necessary to look at the shape of the
shaft’s path (known as its ‘orbit’) to describe fully the vibration, before
deciding a level that is deemed acceptable for turbocompressor operation.
These principles are reflected in the way that shaft vibration levels are
assessed under VDI 2059. The important points are shown in Fig. 8.5. Note
the annotations that show how the maximum recorded displacement in the x
and y planes are resolved to give a resultant value. This standard includes
guidance on acceptance levels. There are three classes designated: A (the
most stringent), B and C for absolute (the so-called criteria I value)
displacement levels, and a single acceptance level for the amount by which
displacement levels change during the test.
The performance test
The main aspects of interest are:
• the discharge pressure/volume characteristic: the objective is to
demonstrate whether the machine will reach the specified volume
throughput of gas at the required discharge pressure, without surging;
• the turn-down ratio to demonstrate that the flow modulation vanes can be
adjusted sufficiently to reach the minimum rated throughput;
• mechanical integrity: vibration levels must be controlled on such high-
speed machines, and the turbocompressor needs to be able to run
continuously without any significant wear or deterioration;
Engineers’ Guide to Rotating Equipment196
Fig. 8.5 Shaft vibration – the essential points of VDI 2059
Compressors and Turbocompressors 197
• noise level normally with an acoustic enclosure
• efficiency or power consumption, depending on the exact form of
specification used.
Table 8.5 shows a typical set of performance guarantees expressed for such
a low-discharge pressure air sparging turbocompressor.
Table 8.5 Low-pressure turbocompressor:
typical performance guarantees
Single-stage turbocompressor, aircooled with variable diffuser guide vanes.
Motor speed 3000 r/min with single helical step-up gearbox to impeller speed
of 22 900 r/min. Skid-mounted with integral oil tank and acoustic sound
enclosure.
Medium Atmospheric air
Inlet temperature 28 °CThe inlet conditions
Inlet pressure 1013 mBar (absolute)
Relative humidity 100%
Gas constant 288.9 Nm/kg/KAssumptions
Isentropic index 1.4
Volume flow Minimum 5000 m3/h
(measured at suction) (83.3 m3/min)Performance requirementsMaximum 11 000 m3/h
(183.3 m3/min)
Discharge pressure 2 bar absolute without
surging (approx. 10 m
‘water gauge’)
Power consumption 320 kW (+3% tolerance)
Noise 85 dB(A) 1 m from
enclosure
Performance test to VDI 2045 with vibration Test standard
assessment to VDI 2059 Class B
The test arrangement
The most common type of turbocompressor performance test is carried
out ‘open-circuit’ using air, hence using atmospheric air as a near-
approximation to the specified suction conditions. The test circuit
arrangement for this is shown in VDI 2045 and the other relevant technical
standards and is summarized in Figs 8.6 and 8.7.
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Fig. 8.6 Turbocompressor performance test – typical test circuit
Compressors and Turbocompressors 199
Flowrates are measured by four tappings, equispaced around the
circumference of the pipe and interconnected by a loop. This gives an
accurate ‘averaged’ pressure reading to feed to the water gauge manometer.
The performance test routine
Figure 8.8 shows typical performance test results. Note how the maximum
throughput, minimum (turn-down) point, and power consumption at full
load all meet the guarantee points as they are shown on the graph.
Vibration measurements
VDI 2059 uses the concept of relative shaft vibration as the acceptance
parameter for turbocompressor vibration. The non-contacting probes used to
sense this vibration are a permanent fixture, threaded into holes extending
through the bearing housing and sensing from a highly polished area of the
gear shaft. Figure 8.9 shows the typical location of the vibration sensors.
Both sensing positions are located on the high-speed pinion shaft, and
measurement is recorded in two perpendicular planes (x and y) at each
location. The measured parameter is vibration displacement s (µm).
Fig. 8.7 Turbocompressor performance test –
flow measurement
Engineers’ Guide to Rotating Equipment200
Fig. 8.8 Turbocompressor – typical ‘performance map’
test results
Compressors and Turbocompressors 201
Location of axial
position sensor (if fitted)
Note: remember that
these are relative shaft
vibrations to VDI 2059,
not ‘housing’ vibrations
as in VDI 2056
You can ignore
transient vibrations
at low frequencies
Shaft vibration sensors S1
and S2 both monitor the
(high speed) pinion shaft
S1 S2x-plane
7 µm
12 µm
4 µm
5 µm
S1 (x-plane)
S1 (y-plane)
S2 (x)
S2 (y)
30 000 Hz
Speed (frequency)
20 000
Dis
pla
cem
ent
S (
µm)
10 000 Rated
speed
To check if the results are acceptable:
Smax = √( x2 + y
2) = √(72 + 122) = 13.9µm
Compare this to the acceptable level B from Fig. 8.5 = 30 µm, so the
results are acceptable to VDI 2059 Class B.
Checking the displacement change from VDI 2059, (and Fig. 8.5)
B = smaller of B or ( N + 025 B) ie 30 µm or (13.9 + 30/4) = 21 µm
So B* = 21 µm: the greatest ‘change’ from the above results is
(12 – 4) = 8 µm, hence the results are acceptable.
S
SSSS
S
SS
Fig. 8.9 Turbocompressor vibration tests
Engineers’ Guide to Rotating Equipment202
Displacement measurements are plotted against frequency scanning from
0 Hz up to a frequency corresponding to rotational speed of the pinion shaft
– 22 900 r/min in this example. Figure 8.9 shows typical results – the
various ‘transient’ displacements at very low frequencies can safely be
ignored. The largest displacements will show as prominent ‘peaks’ on the
trace, normally close to a fraction of the rotational frequency. It is unusual
for both sensing positions on the pinion shaft to show the same displacement
values: the sensor nearer the impeller will generally show the highest
reading (as in Fig. 8.9). This is caused by ‘imposed vibration’ from
the impeller, which experiences various hydrodynamic instabilities,
exaggerated by its high rotational speed.
Under VDI 2059 there are two ‘acceptance criteria’: the maximum
displacement level Smax (the so-called ‘criterion I’) and the acceptable
‘displacement change’ (criterion II). Figure 8.5 shows how to calculate
these. Note how some simple assumptions have to be made as to what is
considered the ‘nominal’ maximum displacement.
Noise measurement
Turbocompressors are inherently noisy machines, up to about 98 dB(A) for
the highest tip speed versions, so they are nearly always fitted inside an
acoustic enclosure to reduce the noise to manageable levels. A guarantee
figure of 85 dB(A) outside the enclosure is normal.
The principles of noise measurement are broadly the same as used for gas
turbines, i.e. the measurement of the A-weighted average at a distance of
1 m from the turbocompressor ‘reference surface’.
CHAPTER 9
Prime Movers
9.1 Steam turbinesSteam turbines are complex items of rotating equipment. They can be very
large, up to 1500 MW capacity with LP rotor diameters of several metres,
introducing a variety of technical challenges related to large components
and heavy material sections. Some typical design criteria that have to be
overcome are:
• High superheat temperatures and pressures, with the corresponding high
specification material choices.
• Thicker material ‘ruling’ sections in the casing parts. This attracts a
number of particular material defects more likely to occur in thick, cast
sections.
• Longer unsupported rotor lengths. This gives a greater tendency for
bending and subsequent vibration, particularly on single-shaft machines.
• Larger diameters, particularly of the LP rotors, in which most of the stress
on a blade is caused by centrifugal force rather than steam load. Higher
stresses mean a greater sensitivity to defect size, requiring more searching
NDT techniques on the rotating components.
Operating systems
Steam turbines incorporate several complex operating systems.
Lubricating oil (LO) system
Figure 9.1 shows a basic schematic diagram of a steam turbine LO system.
LO pressure is maintained in the bearing galleries by means of pumps and a
constant-pressure valve. Tube- or plate-type heat exchangers coupled with
an automatic temperature control valve regulate the temperature. The LO
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Fig. 9.1 Steam turbine LO system – schematic
Prime Movers 205
drain tank underneath the turbine is designed with sufficient volume and
residence time to allow the oil to de-aerate before being pumped back to the
bearings. This tank is maintained at a slight vacuum by a vapour extraction
fan that exhausts to atmosphere. A gear pump driven off the turbine shaft
provides design LO flow at shaft speeds greater than about 80 per cent of
full speed; at lower speeds, the flow is supplemented by electric pumps. A
smaller capacity (approximately 60 per cent flow) back-up electric (usually
DC battery-operated) pump is provided to supplement flow during system
power failures. The steam turbine bearings are fed via individual oil supply
lines fitted with orifice plates. On discharge from the bearings, the oil drains
into the bearing pedestals through sight glasses. Temperature and pressure
supervision is used to monitor running conditions.
Jacking oil
Jacking oil is used to pressurize the bearings and thereby reduce the friction
coefficient between the turbine shaft and the bearings during start-up and
shut-down of the turbine. Pressure is supplied by a separate positive
displacement (normally a variable displacement swash-plate piston-type)
jacking oil pump. The pump cuts in and out automatically when the shaft
reaches pre-set rotational speeds. Figure 9.2 shows a schematic arrangement
of a typical steam turbine jacking oil system.
Hydraulic system
Most steam turbine designs are fitted with a hydraulic oil system that
operates the various steam admission and control valves. The system
comprises triple-rotor positive displacement screw pumps supplying
through a duplex filter/regeneration and a pilot-operated constant-pressure
valve arrangement. An in-line accumulator may be used to provide a
pressure ‘reservoir’ in the system. The system is normally totally separate
from the turbine-lubricating oil, and uses a special grade of hydraulic fluid
operating at pressures up to about 40 bar g.
The hydraulic system is used to power the turbine safety and protection
system (TSPS). This is an electronically operated system that operates the
steam inlet ‘intercept’ valves via electrohydraulic transducers. Figure 9.3
shows a simplified schematic. The entire system works on a fail-safe
principle, i.e. the hydraulic pressure acts to keep the steam valves open. The
trip system uses 2-out-of-3 channel logic in which operation of two trip-
signal sensors is sufficient to depressurize the system and thereby trip the
turbine. The trip functions are restricted during normal transient start-up and
shut-down sequences of the turbine in order to avoid spurious trips.
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From lubricating
oil tank
Fig. 9.2 Steam turbine jacking oil system – schematic
Prime Movers 207
Gland steam system
All steam turbines are fitted with a gland steam system (Fig. 9.4) that stops
steam leakage along the turbine shafts and prevents air being drawn into
low-pressure areas, destroying the vacuum. The normal method used is non-
contact labyrinth seals (see Fig. 9.5). The quality of the gland steam under
all operating conditions of the turbine is controlled by an admission valve.
Excess superheat temperature is reduced by means of water sprays or a
similar desuperheating arrangement. Under conditions of high turbine load,
excess gland steam is routed to the condenser by an automatic dump valve.
Vacuum breaker
Steam turbines are fitted with a ‘vacuum breaking’, electrically actuated
butterfly valve that opens to allow air to enter the condenser during the run-
down period when the turbine rotor is coasting to a stop. The admission of
air destroys the vacuum and provides a resistance to the rotor, thereby
stopping it more quickly and avoiding extended periods of operation at
Fig. 9.3 Steam turbine hydraulic oil system – schematic
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Fig. 9.4 Steam turbine gland steam system – schematic
Prime Movers 209
critical speeds, which would cause excessive vibration and resultant high
rotor stresses and bearing wear. The vacuum breaking valve opens
progressively so that full atmospheric pressure is not restored in the turbine
casing until shaft speed has fallen to less than about 50 per cent of rated
speed. This avoids excessive stresses in the lower pressure stages of the
turbine blades.
Turbine drains system
Turbine casing drain valves are installed to drain the casing during periods
of start-up and transient operation, thereby helping to minimize damage
from water hammer and excessive thermal stresses. Separate drain lines are
used to drain condensate from specific areas during, for example, start-up.
Drain valves are normally pneumatically controlled and are divided into
external drains, which drain to an external atmospheric vessel and operate
when the turbine is at standstill, and internal drains, which drain to an
integral flash box, and operate only when the rotor is moving. Automatic
drains are normally set to close when the turbine has reached approximately
15–20 per cent of full load.
Fig. 9.5 Steam turbine labyrinth seals
Engineers’ Guide to Rotating Equipment210
Supervision systems
The turbine supervision consists of a number of electronic systems that
monitor the following parameters (see Fig. 9.6):
• turbine rotational speed;
• shaft axial position relative to the casing;
• bearing housing and shaft vibration;
• absolute and differential expansions;
• rotor eccentricity.
Fig. 9.6 Steam turbine supervision system – schematic
A reference ‘zero’ position of the rotor is fixed using a ‘key phasor’ position
sensor. Rotational speed is measured by three non-contact probes. Axial
displacement of the rotor is measured by inductive sensors located in the
thrust (axial) bearing housing. Housing and shaft vibration is sensed using
the principles shown in Chapter 4 and referred to by ISO 1940 or API
standard limits. Figure 9.7 shows a typical monitoring arrangement.
‘Absolute expansion’ in steam turbines is a measure of sudden variations
in expansion that do not correspond to thermal transients taking place at the
time. Figure 9.8 shows the method of absolute and differential expansion
measurements at the bearing pedestals.
Prime Movers 211
Fig. 9.7 Steam turbine vibration monitoring
Fig. 9.8 Steam turbine expansion measurement
Engineers’ Guide to Rotating Equipment212
Specifications and standards
Technical standards relating to steam turbines fall into three main
categories.
The generalized technology standards
These provide a broad coverage of design, manufacture, and testing. Two
important ones are API 611: (1989) General purpose steam turbines for
refinery service and API 612: (1987) Special purpose steam turbines for
refinery service. ASME/ANSI PTC (Power Test Codes) No. 6 is a related
document group that complements the API standards.
Performance test standards
These cover only the performance testing of turbines under steaming
conditions. They are used for performance verification after commissioning
on site, but not for works testing. They are BS 5968: (1980) (similar to IEC
46-2) and BS 752: (1974) (similar to IEC 46-1) Test code for acceptance
tests.
Procurement standards
The predominant document is BS EN 60045-1: (1993) Steam turbine
procurement – identical to IEC 45-1. It has been recently updated and
encompasses many of the modern practices governing the way in which
steam turbines are specified and purchased. Some important parts of the
content are:
• it provides clear guidance on governor characteristics and overspeed
levels;
• vibration is addressed in two ways: bearing housing vibration using VDI
2056/ISO 2372: (1984) (using mm/s as the guiding parameter), and shaft
vibration using ISO 7919: (1986) and the concept of relative displacement
measurement;
• definitive requirements are stated for hydrostatic tests on the pressurized
components of the turbine.
Turbine hydrostatic test
The predominant design criterion for turbine casings is the ability to resist
hoop stress at the maximum operating temperature. For practical reasons, a
hydrostatic test is carried out at ambient temperature. Some important points
are given below.
• The test pressure is normally 150 per cent of the maximum allowable
pressure the casing will experience in service. It is sometimes necessary
Prime Movers 213
to apply a multiplying factor to compensate for the difference in tensile
strength of the steel between ambient and operating temperature.
Practically, codes such as ASME Section VIII Division 1 are used to
determine material stresses and the corresponding test pressure.
• Some types of casing (typically those that have been designed to very
‘tight’ stress criteria) are tested by sub-dividing the casing with steel
diaphragms held in place by jacks. This enables the various regions of the
casing to be tested at individual pressures that are more representative of
the pressure gradient the casing experiences in use. Figure 9.9 shows such
an arrangement.
• Hydrostatic pressure is maintained for a minimum of 30 min with two
gauges fitted to identify any pressure drops.
Fig. 9.9 Steam turbine casing hydrostatic test
Engineers’ Guide to Rotating Equipment214
Some important visual inspection points are:
• Flange faces. After the hydrostatic test, it is important to check the
flatness of the flange-faces (using marking blue) to make sure no
distortion has occurred. Pay particular attention to the inside edges; this is
where distortion often shows itself first. Any ‘lack of flatness’ means that
the faces must be skim milled.
• Bolt-holes. Visually check around all the flange bolt-holes for cracks.
• Internal radii. Check that small radii inside the casing have been well
dressed and blended to minimize stress concentrations.
• General surface finish. There should be a good ‘as-cast’ finish on the
inside of the casing without significant surface indentations. The visual
inspection standard MSS-SP-55 is used as a broad guide.
Rotor tests
Steam turbine rotors are subject to dynamic balancing, overspeed, and tests
on vibration assembly using similar techniques to those for gas turbine and
gearbox rotors.
Dynamic balancing
This is carried out after the blades have been assembled, normally at low
speed (400–500 r/min). Smaller HP and IP rotors will have two correction
planes for adjustment weights, while large LP rotors have three.
API 611/612 specifies a maximum residual unbalance U per plane of
U (g.mm) =
where
W = journal load in kg
N = maximum continuous speed in r/min
ISO 1940 specifies its balance quality grade G2.5 for steam turbine rotors.
A similar approach is adopted by VDI 2060.
Vibration
API 611/612 specifies vibration as an amplitude. The maximum peak-to-
peak amplitude A (microns) is given by: A (µm) = 25.4 √(12 000/N) with an
absolute limit of 50 µm. BS EN 60045-1 adopts the same approach as other
European turbine standards. Bearing housing vibration follows ISO 2372
(similar to VDI 2056) using a velocity V (r.m.s.) criterion of 2.8 mm/s. Shaft
vibration is defined in relation to ISO 7919-1, which is a more complex
approach.
6350 (kg)
(r/min)
W
N
Prime Movers 215
Overspeed
Steam turbine rotor overspeed tests are carried out in a vacuum chamber to
minimize problems due to windage. API 611/612 infers that a steam turbine
rotor should be overspeed tested at 110 per cent of rated speed. BS EN
60045-1 places a maximum limit of 120 per cent of rated speed for the
overspeed test. In practice, this is more usually 110 per cent.
Assembly tests
Most steam turbine clearances are measured before fitting the outer turbine
casing top half. Figure 9.10 shows the locations at which the main
clearances are taken and gives indicative values for a double-casing type HP
turbine. Note the following points.
• Gland clearances Radial and axial clearances are normally larger at the
low-pressure (condenser) end. The readings should be confirmed at four
diametral positions.
• Nozzle casing and balance piston seals The axial clearances are generally
approximately three times the radial clearances.
• Blade clearances These are measured using long (300–400 mm) feeler
gauges to take clearance measurements at the less accessible radial
locations. Note how the radial and axial clearances (and the allowable
tolerances) increase towards the low-pressure end.
Radial clearances for the rotating blades tend to be broadly similar to those
for the stationary blades. However, lower temperature turbines in which the
fixed blades are carried in cast steel diaphragms may have smaller
clearances for the labyrinth seal between the diaphragm and the rotor (this
is due to the high-pressure drop across the impulse stages).
Engineers’ Guide to Rotating Equipment216
Fig. 9.10 Steam turbine – typical HP turbine clearances
Prime Movers 217
Useful standards
Table 9.1 contains published technical standards with particular reference to
turbines.
Table 9.1 Technical standards – turbines
Standard Title Status
BS 3135: 1989,
ISO 2314: 1989
Specification for gas turbine
acceptance test.
Current
BS 3863: 1992,
ISO 3977: 1991
Guide for gas turbines procurement. Current, work
in hand
BS 5671: 1979,
IEC 60545: 1976
Guide for commissioning, operation,
and maintenance of hydraulic
turbines.
Current
BS 5860: 1980,
IEC 60607: 1978
Method for measuring the efficiency
of hydraulic turbines, storage pumps,
and pump turbines (thermodynamic
method).
Current
BS 7721: 1994,
ISO 10494: 1993
Gas turbines and gas turbine sets.
Measurement of emitted airborne
noise. Engineering/survey method.
Current
BS 7854-2: 1996,
ISO 10816-2: 1996
Mechanical vibration. Evaluation of
machine vibration by measurements
on non-rotating parts. Large land-
based steam turbine generator sets
in excess of 50 MW.
Current, work
in hand
BS 7854-3: 1998,
ISO 10816-3: 1998
Mechanical vibration. Evaluation of
machine vibration by measurements
on non-rotating parts. Industrial
machines with nominal power above
15 kW and nominal speeds between
120 r/min and 15 000 r/min when
measured in situ.
Current
BS 7854-4: 1998,
ISO 10816-4: 1998
Mechanical vibration. Evaluation of
machine vibration by measurements
on non-rotating parts. Gas turbine
driven sets excluding aircraft
derivatives.
Current
BS ISO 7919-2: 1996 Mechanical vibration of non-
reciprocating machines.
Measurements on rotating shafts and
evaluation criteria. Large land-based
steam turbine generator sets.
Current, work
in hand
Engineers’ Guide to Rotating Equipment218
BS ISO 7919-3: 1996 Mechanical vibration of non-
reciprocating machines.
Measurements on rotating shafts and
evaluation criteria. Coupled industrial
machines.
Current
BS ISO 7919-4: 1996 Mechanical vibration of non-
reciprocating machines.
Measurements on rotating shafts and
evaluation criteria. Gas turbine sets.
Current
BS ISO 7919-5: 1997 Mechanical vibration of non-
reciprocating machines.
Measurements on rotating shafts and
evaluation criteria. Machine sets in
hydraulic power generating and
pumping plants.
Current
BS ISO 11042-1: 1996 Gas turbines. Exhaust gas emission.
Measurement and evaluation.
Current
BS ISO 11042-2: 1996 Gas turbines. Exhaust gas emission.
Automated emission monitoring.
Current
BS ISO 11086: 1996 Gas turbines. Vocabulary. Current
BS ISO 14661: 2000 Thermal turbines for industrial
applications (steam turbines, gas
expansion turbines). General
requirements.
Current
BS IEC 61366-1: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. General and annexes.
Current
BS IEC 61366-2: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. Guidelines for technical
specifications for Francis turbines.
Current
BS IEC 61366-3: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. Guidelines for technical
specifications for Pelton turbines.
Current
BS IEC 61366-4: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. Guidelines for technical
specifications for Kaplan and
propeller turbines.
Current
BS IEC 61366-5: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. Guidelines for technical
specifications for tubular turbines.
Current
Table 9.1 Cont.
BS IEC 61366-6: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. Guidelines for technical
specifications for pump turbines.
Current
BS IEC 61366-7: 1998 Hydraulic turbines, storage pumps,
and pump turbines. Tendering
documents. Guidelines for technical
specifications for storage pumps.
Current
BS EN 45510-2-6:
2000
Guide for the procurement of power
station equipment. Electrical
equipment. Generators.
Current
BS EN 45510-5-1:
1998
Guide for the procurement of power
station equipment. Steam turbines.
Current
BS EN 45510-5-2:
1998
Guide for the procurement of power
station equipment. Gas turbines.
Current
BS EN 45510-5-3:
1998
Guide for the procurement of power
station equipment. Wind turbines.
Current
BS EN 45510-5-4:
1998
Guide for the procurement of power
station equipment. Hydraulic turbines,
storage pumps, and pump turbines.
Current
BS EN 45510-6-4:
2000
Guide for the procurement of power
station equipment. Turbine
auxiliaries. Pumps.
Current
BS EN 45510-6-9:
2000
Guide for the procurement of power
station equipment. Turbine
auxiliaries. Cooling water systems.
Current
BS EN 60034-3: 1996 Rotating electrical machines. Specific
requirements for turbine-type
synchronous machines.
Current
BS EN 60041: 1995 Field acceptance tests to determine
the hydraulic performance of
hydraulic turbines, storage pumps,
and pump turbines.
Current
BS EN 60045-1: 1993,
IEC 60045-1: 1991
Guide to steam turbine procurement. Current
BS EN 60953-1: 1996,
IEC 60953-1: 1990
Rules for steam turbine thermal
acceptance tests. High accuracy for
large condensing steam turbines.
Current
BS EN 60953-2: 1996,
IEC 60953-2: 1990
Rules for steam turbine thermal
acceptance tests. Wide range of
accuracy for various types and sizes
of turbines.
Current
Prime Movers 219
Table 9.1 Cont.
Engineers’ Guide to Rotating Equipment220
BS EN 60994: 1993,
IEC 60994: 1991
Guide for field measurement of
vibrations and pulsations in hydraulic
machines (turbines, storage pumps,
and pump turbines).
Current
BS EN 60995: 1995,
IEC 60995: 1991
Determination of the prototype
performance from model acceptance
tests of hydraulic machines with the
consideration of scale effects.
Current
DD ENV 61400-1:
1995
Wind turbine generator systems.
Safety requirements.
Current
BS EN 61400-2: 1996,
IEC 61400-2: 1996
Wind turbine generator systems.
Safety of small wind turbines.
Current
BS EN 61400-11:
1999,
IEC 61400-11: 1998
Wind turbine generator systems.
Acoustic noise measurement
techniques.
Current, work
in hand
BS EN 61400-12:
1998,
IEC 61400-12: 1998
Wind turbine generator systems.
Wind turbine power performance
testing.
Current
95/701797 DC Technical report for the nomenclature
of hydraulic machinery
(IEC/CD4/112/CDV).
Current, draft
for public
comment
95/713333 DC Gas turbines. Procurement. Part 1.
General and definitions (ISO/DIS
3977-1).
Current, draft
for public
comment
95/713334 DC Gas turbines. Procurement. Part 2.
Standard reference conditions and
ratings (ISO/DIS 3977-2).
Current, draft
for public
comment
96/704522 DC Gas turbines. Procurement. Part 11.
Reliability, availability, maintainability,
and safety (ISO/DIS 3977-11).
Current, draft
for public
comment
97/703272 DC Hydraulic turbines, storage pumps,
and pump turbines. Hydraulic
performance. Model acceptance
tests (IEC 193-2).
Current, draft
for public
comment
97/704872 DC Gas turbines. Procurement. Part 7.
Technical information (ISO/CD 3977-
7).
Current, draft
for public
comment
97/704873 DC Gas turbines. Procurement. Part 8.
Inspection, testing, installation, and
commissioning (ISO/CD 3877-8).
Current, draft
for public
comment
97/710296 DC Gas turbines. Procurement. Part 6.
Combined cycles (ISO 3977-6).
Current, draft
for public
comment
Table 9.1 Cont.
98/709429 DC ISO/CD 3977-4.2. Gas turbines.
Procurement. Part 4. Fuels and
procurement (ISO/CD 3977-4.2).
Current, draft
for public
comment
98/711877 DC Centrifugal pumps for petroleum,
heavy-duty chemical, and gas
industries services (ISO/DIS 13709).
Current, draft
for public
comment
98/716323 DC Mechanical vibration. Evaluation of
machine vibration by measurements
on non-rotating parts. Part 5.
Machine sets in hydraulic power
generating and pumping plants
(ISO/DIS 10816-5).
Current, draft
for public
comment
99/200755 DC IEC 61400-22. Wind turbine
certification (IEC Document
88/102/CD).
Current, draft
for public
comment
99/204720 DC IEC 61400-23 TS Ed. 1. Wind
turbine generator systems. Part 23.
Full-scale structural testing of rotor
blades for WTGSs (IEC Document
88/116/CDV).
Current, draft
for public
comment
99/710366 DC IEC 4/155/CD. Hydraulic turbines.
Testing of control systems.
Current, draft
for public
comment
00/200785 DC IEC 61400-13. Wind turbine
generator systems. Part 13.
Measurement of mechanical loads
(IEC Document 88/120/CDV).
Current, draft
for public
comment
00/702245 DC ISO 10437. Petroleum and natural
gas industries. Special purpose
steam turbines for refinery service.
Current, draft
for public
comment
00/704175 DC ISO/DIS 7919-2. Mechanical
vibration. Evaluation of machine
vibration by measurements on
rotating shafts. Part 2. Land-based
steam turbines and generators in
excess of 50 MW with normal
operating speeds of 1500 r/min,
1800 r/min, 3000 r/min, and 3600
r/min.
Current, draft
for public
comment
Prime Movers 221
Table 9.1 Cont.
Engineers’ Guide to Rotating Equipment222
00/704176 DC ISO/DIS 10816-2. Mechanical
vibration. Evaluation of machine
vibration by measurements on non-
rotating parts. Part 2. Large land-
based steam turbines and generators
in excess of 50 MW with normal
operating speeds of 1500 r/min,
1800 r/min, 3000 r/min, and 3600
r/min.
Current, draft
for public
comment
00/704290 DC IEC 60953-3/Ed. 1 Rules for steam
turbine thermal acceptance tests.
Part 3. Thermal performance
verification tests of retrofitted steam
turbines.
Current, draft
for public
comment
00/704918 DC ISO/DIS 3977-6. Gas turbines.
Procurement. Part 6. Combined
cycles.
Current, draft
for public
comment
00/712064 DC ISO/DIS 102: 2000. Aircraft. Gravity
filling orifices and nozzles.
Current, draft
for public
comment
BS 132: 1983 Guide for steam turbines
procurement.
Withdrawn,
superseded
BS 489: 1983 Specification for turbine oils. Withdrawn,
revised
BS 752: 1974 Test code for acceptance of steam
turbines.
Withdrawn,
superseded
BS 3135: 1975,
ISO 2314-1973
Specification for gas turbines:
acceptance tests.
Withdrawn,
revised
BS 3853: 1966 Specification for mechanical
balancing of marine main turbine
machinery.
Withdrawn,
superseded
BS 3863: 1979,
ISO 3977-1978
Guide for gas turbines procurement. Withdrawn,
revised
BS 5000: Part 2: 1988 Rotating electrical machines of
particular types or for particular
applications. Specification for turbine-
type synchronous machines.
Withdrawn,
revised
BS 5968: 1980 Methods of acceptance testing of
industrial-type steam turbines.
Withdrawn,
superseded
Table 9.1 Cont.
Prime Movers 223
9.2 Gas turbines – aeroderivatives Although there are many variants of gas turbine-based aeroderivative
engines, they operate using similar principles. Air is compressed by an axial
flow or centrifugal compressor. The highly compressed air then passes to a
combustion chamber where it is mixed with fuel and ignited. The mixture of
air and combustion products expands into the turbine stage, which in turn
provides the power through a coupling shaft to drive the compressor. The
expanding gases then pass out through the engine tailpipe, providing thrust,
or can be passed through a further turbine stage to drive a propeller or
helicopter rotor. For aeronautical applications the two most important
criteria in engine choice are thrust (or power) and specific fuel consumption.
Figure 9.11 shows an outline of the main types and Table 9.2 gives the
terminology.
Table 9.2 Gas turbine propulsion terminology
Gas turbine (GT) Engine comprising a compressor and turbine. It produces
jet thrust and/or shaft ‘horsepower’ output via a power
turbine stage.
Turbojet A GT which produces only jet thrust (i.e. no power turbine
stage). Used for jet aircraft.
Turboprop A GT that produces shaft output and some jet thrust. Used
for propeller-driven aircraft.
Afterburner A burner which adds fuel to the later stages of a GT to give
increased thrust. Used for military aircraft.
Pulsejet A turbojet engine with an intermittent 'pulsed' thrust output.
Ramjet An advanced type of aircraft GT which compresses the air
using the forward motion (dynamic head) of the engine.
Rocket motor A 'jet' engine that carries its own fuel and oxygen supply.
Produces pure thrust when there is no available oxygen
(e.g. space travel).
The simple turbojet
The simple turbojet derives all of its thrust from the exit velocity of the
exhaust gas. It has no separate propeller or ‘power’ turbine stage.
Performance parameters are outlined in Fig. 9.12. Turbojets have poor fuel
economy and high exhaust noise. The fact that all the air passes through the
engine core (i.e. there is no bypass) is responsible for the low propulsive
efficiency, except at very high aircraft speed. The Concorde supersonic
Engineers’ Guide to Rotating Equipment224
Fig. 9.11 Aero gas turbines – main types
Prime Movers 225
transport (SST) aircraft is virtually the only commercial airliner that still
uses the turbojet. By making the convenient assumption of neglecting
Reynolds number, the variables governing the performance of a simple
turbojet can be grouped as shown in Table 9.3.
Fig. 9.12 Aero turbojet – typical performance parameters
Engineers’ Guide to Rotating Equipment226
Table 9.3 Turbojet performance parameter groupings
Non-dimensional group Uncorrected Corrected
Flight speed V0/√t0 V0/√θRPM N/√T N/√θAir flow rate Wa/√(T/D2
P) Wa/√(θ/δ)
Thrust F/D2P F/δFuel flow rate WfJ∆Hc/D
2P√T Wf/δ√θ
where
θ = T/Tstd = T/519 (T/288) = corrected temperature
δ = P/pstd = P/14.7 (P/1.013 × 105) = corrected pressure
Wf = fuel flow
Turbofan
Most large airliners and subsonic aircraft are powered by turbofan engines.
Typical commercial engine thrust ratings range from 7000 lb (31 kN) to
90 000 lb (400 kN+), suitable for large aircraft such as the Boeing 747. The
turbofan is characterized by an oversized fan compressor stage at the front
of the engine which bypasses most of the air around the outside of the
engine where it re-joins the exhaust gases at the back, increasing
significantly the available thrust. A typical bypass ratio is 5–6 to 1.
Turbofans have better efficiency than simple turbojets because it is more
efficient to accelerate a large mass of air moderately through the fan to
develop thrust, than to highly accelerate a smaller mass of air through the
core of the engine to develop the same thrust. Figure 9.13 shows the basic
turbofan and Fig. 9.14 its two- and three-spool variants. The two-spool
arrangement is the most common, with a single-stage fan plus turbine on the
low-pressure rotor and an axial compressor plus turbine on the high-
pressure rotor. Many turbines are fitted with thrust-reversing cowls that act
to reverse the direction of the slipstream of the fan bypass air.
..
..
.
Prime Movers 227
Fig. 9.13 The basic aero turbofan
Two-spool (most common aero engine configuration)
Core nozzle
Bypass nozzleLPT
HPT
LPC
Fa
n
HPC
Fan
IPCHPC
HPT
LPT
IPT
Three-spool engine (Rolls Royce RB211)
High-pressure spool – The hp
turbine (HPT) drives the high-
pressure compressor (HPC)
Low-pressure spool – The lp
turbine (LPT) drives the low-
pressure compressor (LPC)
Fig. 9.14 Aero turbanfan – two- and three-spool variants
Engineers’ Guide to Rotating Equipment228
Turboprop
The turboprop configuration is typically used for smaller aircraft. The
engine (see Fig. 9.11) uses a separate power turbine stage to provide torque
to a forward-mounted propeller. The propeller thrust is augmented by gas
thrust from the exhaust. Although often overshadowed by the turbofan,
recent developments in propeller technology mean that smaller airliners
such as the SAAB 2000 (2 × 4152 hp [3096 kW] turboprops) can compete
on speed and fuel cost with comparably-sized turbofan aircraft. The most
common turboprop configuration is a single shaft with centrifugal
compressor and integral gearbox. Commuter airliners often use a two- or
three-shaft ‘free turbine’ layout.
Propfans
Propfans are a modern engine arrangement specifically designed to achieve
low fuel consumption. They are sometimes referred to as ‘inducted’ fan
engines. The most common arrangement is a two-spool gas generator and
aft-located gearbox driving a ‘pusher’ fan. Historically, low fuel prices have
reduced the drive to develop propfans as commercially viable mainstream
engines. Some Russian aircraft, such as the Anotov An-70 transport design,
have been designed with propfans.
Turboshafts
Turboshaft engines are used predominantly for helicopters. A typical
example, such as the Rolls-Royce Turbomeca RTM 32201, has a three-stage
axial compressor directly coupled to a two-stage compressor turbine, and a
two-stage power turbine. Drive is taken off the power turbine shaft, through
a gearbox, to drive the main and tail rotor blades. Figure 9.11 shows the
principle.
Ramjet
This is the crudest form of jet engine. Instead of using a compressor it uses
the ‘ram effect’ obtained from its forward velocity to accelerate and
pressurize the air before combustion. Hence, the ramjet must be accelerated
to speed by another form of engine before it will start to work. Ramjet-
propelled missiles, for example, are released from moving aircraft or
accelerated to speed by booster rockets. A supersonic version is the
‘scramjet’ which operates on liquid hydrogen fuel.
Prime Movers 229
Pulsejet
A pulsejet is a ramjet with an air inlet that is provided with a set of shutters
fixed to remain in the closed position. After the pulsejet engine is launched,
ram air pressure forces the shutters to open, and fuel is injected into the
combustion chamber and burned. As soon as the pressure in the combustion
chamber equals the ram air pressure, the shutters close. The gases produced
by combustion are forced out of the jet nozzle by the pressure that has built
up within the combustion chamber. When the pressure in the combustion
chamber falls off, the shutters open again, admitting more air, and the cycle
repeats.
Aero engine data
Table 9.4 shows indicative design data for commercially available aero
engines from various manufacturers.
Engin
eers
’G
uid
e to
Rota
ting E
quip
ment
230
Company Allied
signal
CFE CFMI General Electric (GE) IAE (PW, RR, MTU, JAE)
Engine
type/model
LF507 CFE738 CFM 56
5C2
CF34
3A,3B
CF6
80A2
CF6
80C2-B2
CF6
80E1A2
GE 90
85B
V2500
A1
V2522
A5
V2533
A5
Aircraft BA146-300
Avro RJ
Falcon
2000
A340 Canadair
RJ
A310-200
B767-200
B767-
200ER
A330 B777-
200/300
A320
A319
MD90-10/30
A319
A321-200
In service date 1991 1992 1994 1996 1981 1986 1995 1989 1993 1994
Thrust (lb) 7000 5918 31200 9220 60000 52500 67500 90000 25000 22000 33000
Flat rating (°C) 23.0 30.0 30.0 33.3 32.0 30.0 30.0 30.0 30.0 30.0
Bypass ratio 5.60 5.30 6.40 5.40 5.00 4.60
Pressure ratio 13.80 23.00 31.50 21.00 27.30 27.10 32.40 39.30 29.40 24.9 33.40
Mass flow (lb/s) 256 240 1065 1435 1650 1926 3037 781 738 848
SFC (lb/hr/lb) 0.406 0.369 0.32 0.35 0.35 0.32 0.33 0.35 0.34 0.37
Climb
Max thrust (lb) 7580 12650 18000 5620 5550 6225
Flat rating (°C) ISA+10 ISA+10 ISA+10
Cruise
Altitude (ft) 40000 35000 35000 35000 35000 35000 35000 35000
Mach number 0.80 0.80 0.80 0.80 0.83 0.80 0.80 0.80
Thrust (lb) 1310 11045 12000 5070 5185 5725
Thrust lapse rate 0.221 0.229 0.202 0.2 0.174
Flat rating (°C) ISA+10 ISA+10 ISA+10
SFC (lb/hr/lb) 0.414 0.645 0.545 0.623 0.576 0.562 0.545 0.581 0.574 0.574
Table 9.4 Commercial aero engines – data tables
Prim
e M
overs
231
Dimensions
Length (m) 1.620 2.514 2.616 2.616 3.980 4.267 4.343 5.181 3.200 3.204 3.204
Fan diameter (m) 1.272 1.219 1.945 1.245 2.490 2.694 2.794 3.404 1.681 1.681 1.681
Basic eng. weight
(lb)
1385 1325 5700 1670 8496 9399 10726 16644 5210 5252.0 5230.0
Layout
Number of shafts 2 2 2 2 2 2 2 2 2 2 2
Compressor various 1+5LP+-
1CF
1+4LP
9HP
1F+14cHP 1+3LP
14HP
1+4LP
14HP
1+4LP
14HP
1+3LP
10HP
1+4LP
10HP
1+4LP
10HP
1+4LP
10HP
Turbine 2HP 2LP 2HP 3LP 1HP 5LP 2HP 4LP 2HP 4LP 2HP 5LP 2HP 5LP 2HP 6LP 2HP 5LP 2HP 5LP 2HP 5LP
Table 9.4 Cont.
Engin
eers
’G
uid
e to
Rota
ting E
quip
ment
232
Company Pratt and Whitney Rolls-Royce ZMKB
Engine
type/model
PW4052 PW4056 PW4152 PW4168 PW4084 TRENT 772 TRENT 892 TAY 611 RB-211524H D-436T1
Aircraft B767-200
&200ER
B747-400
767-300ER
A310 A330 B777 A330 B777 F100.70
Gulfst V
B747-400
B767-300
Tu-334-1
An 72,74
In service date 1986 1987 1986 1993 1994 1995 1988 1989 1996
Thrust (lb) 52200 56750 52000 68000 84000 71100 91300 13850 60600 16865
Flat rating (°C) 33.3 33.3 42.2 30.0 30.0 30.0 30.0 30.0 30.0 30.0
Bypass ratio 4.85 4.85 4.85 5.10 6.41 4.89 5.74 3.04 4.30 4.95
Pressure ratio 27.50 29.70 27.50 32.00 34.20 36.84 42.70 15.80 33.00 25.20
Mass flow (lb/s) 1705 1705 1705 1934 2550 1978 2720 410 1605
SFC (lb/hr/lb) 0.351 0.359 0.348 0.430 0.563
Climb
Max thrust (lb) 15386 18020 3400 12726
Flat rating (°C) ISA+10 ISA+10 ISA+5 ISA+10
Cruise
Altitude (ft) 35000 35000 35000 35000 35000 35000 35000 35000 36089
Mach number 0.80 0.80 0.80 0.83 0.82 0.83 0.80 0.85 0.75
Thrust (lb) 11500 13000 2550 11813 3307
Thrust lapse rate 0.162 0.142 0.184 0.195 0.196
Flat rating (°C) ISA+10 ISA+10 ISA+10
SFC (lb/hr/lb) 0.565 0.557 0.690 0.570 0.610
Table 9.4 Cont.
Prim
e M
overs
233
Dimensions
Length (m) 3.879 3.879 3.879 4.143 4.869 3.912 4.369 2.590 3.175
Fan diameter (m) 2.477 2.477 2.477 2.535 2.845 2.474 2.794 1.520 2.192 1.373
Basic eng. weight
(lb)
9400 9400 9400 14350 13700 10550 13133 2951 9670 3197
Layout
Number of shafts 2 2 2 2 2 3 3 2 3 3
Compressor 1+4LP
11HP
1+4LP
11HP
1+4LP
11HP
1+5LP
11HP
1+6LP
11HP
1LP 8IP 6HP 1LP 8IP 6HP 1+3LP 12HP 1LP 7IP 6HP 1+1L 6I 7HP
Turbine 2HP 4LP 2HP 4LP 2HP 4LP 2HP 5LP 2HP 7LP 1HP 1IP 4LP 1HP 1IP 5LP 2HP 3LP 1HP 1IP 3LP 1HP 1IP 3LP
Table 9.4 Cont.
Engineers’ Guide to Rotating Equipment234
9.3 Gas turbines – industrialThere are a wide variety of gas turbines (GTs) that have been adapted for
industrial use for power generation and process use.
Basic principles
Figure 9.15 shows the schematic arrangement of an industrial-type GT and
the corresponding graphical representation of a temperature/enthalpy-
entropy (T/h–s) diagram for four main variants: advance sequential
combustion, single combustion, standard design, and aeroderivative type.
Efficiency increases with the area of the ‘enveloping’ process curve.
Fig. 9.15 Industrial gas turbine – schematic arrangement and
T–s/h–s characteristics
Prime Movers 235
Axial flow compressor characteristics
In many industrial GT designs, the combustion air is compressed by an axial
flow compressor attached to the same shaft as the turbine stages. The blade
stages increase the velocity of the air, then convert the resulting kinetic
energy into ‘pressure energy’. The power required to drive the compressor
is derived from the power produced by the subsequent expansion of the gas,
after combustion, through the turbine. Figure 9.16 shows the velocity
relationships across a typical GT compressor stage.
Fig. 9.16 Velocity relationships across a GT compressor stage
Engineers’ Guide to Rotating Equipment236
Axial flow turbine characteristics
Turbine blades are arranged in ‘stages’ that act like a convergent nozzle.
Combustion gas enters the moving blade row with velocity c1, which is
resolved into relative and tangential velocity components w1 and u1,
respectively. The effect of the blades is to increase the relative fluid velocity
component (to w2) without any change to the tangential velocity component
u. Such velocity diagrams (Fig. 9.17) are used to develop the optimum
geometry of blade profiles. Similar diagrams showing axial, radial, and
tangential force components are used to design the overall ruling section
requirements and strength of the rotating and stationary blades.
Gas turbines – major components
Land-based gas turbines for power generation, etc. comprise various major
component systems (see Fig. 9.18). Many are dual fired, i.e. can burn either
natural gas or light distillate oil.
Air intake system
The air intake system comprises an arrangement of mechanical shutters,
filters, silencers, and safety flap valves (see Fig. 9.19). A compressed pulse
air system is installed to provide periodic cleaning of the filters. Anti-icing
hot air can be supplied from the GT compressor stages to prevent freezing
of the inlet regions in cold weather.
The compressor stages
The compressor uses a combination of rotating and stationary blades to
compress the cleaned inlet air prior to combustion. Each pair of stationary
and rotating blades is termed a ‘stage’ and there are typically up to 24 stages
in large, land-based GTs. Compressor blades are located in circumferential
grooves, separated by spacers.
Variable guide vanes (VGVs)
VGVs are movable vanes, installed in rows, which regulate the volume of
air that flows through the compressor.
Blow-off valves
Large blow-off valves are fitted to (normally) two stages of the compressor.
These are necessary during low rotor speed, start-up and shut-down
conditions in order to compensate for flow mismatch between the
compressor and turbine stages by blowing off excess air.
Prime Movers 237
Fig. 9.17 Velocity relationships across a
GT turbine ‘reaction’ stage
Engineers’ Guide to Rotating Equipment238
Combustor arrangement
Fig. 9.18 Industrial GT – general view
Fig. 9.19 GT air intake system
Prime Movers 239
Diffuser
The diffuser is a ring-shaped assembly situated after the last compressor
stage and before the combustion stages.
Combustion system
Advanced high-efficiency designs of land-based GTs use a two-stage
sequential combustion system, loosely termed the environmental vane (EV)
stage and a sequential environmental vane (SEV) stage (see Fig. 9.20). Both
combustion chambers are cooled by air bled off the compressor stages and
distributed through grooves arranged in an annular pattern around the GT
casing. Combustion air flows into the EV combustion zone through inlet
slots and mixes with the fuel gas, which enters via rows of fine holes at the
edge of the slots (or the fuel oil which is sprayed in through a lance). The
fuel is ignited by a separate ignition gas system and electric ignition torches.
The SEV combustion stage is fed with hot gas from the EV stage. Additional
fuel is admitted by the SEV burners which reheat the gas. Separate ignition
is not normally required in the SEV stage as the gases are already hot
enough to ignite the SEV stage fuel. A typical design of 200 MW+ power
generation GT will have 28–32 EV burners and 22–28 SEV burners.
Fig. 9.20 GT sequential combustion arrangement
GT casing
GTs use horizontally split cast steel casings to enclose the vane carriers,
which hold the stator blade assemblies, and the other stationary and rotating
components. The casing incorporates a complex arrangement of cooling
channels, structural reinforcement, and heat/noise insulation. The internal
vane carriers are also split horizontally and protected by heat shields.
Engineers’ Guide to Rotating Equipment240
GT bearings
A series of bearings support the GT shaft (see Fig. 9.21). The turbine ‘hot
end’ journal bearing supports the rotor in the radial direction, while the
compressor ‘cold end’ bearing also takes axial thrust. Bearings are air-
cooled using air bled off from various compressor stages. Sensors (see
Fig. 9.22) detect both axial and radial rotor movement and vibration.
Exhaust gas system
The most common system for land-based GTs is for the hot combustion gas
to be exhausted to a heat recovery steam generator (HRSG) – a large waste-
heat boiler incorporated into a combined cycle system. Gas exhausts from
the GT via an insulated diffuser and silencer, before entering the HRSG or
stack (chimney).
Gas turbine inspections and testing
Acceptance guarantees
Acceptance guarantees for gas turbines are an uneasy hybrid of explicit and
inferred requirements. Most contract specifications contain four explicit
performance guarantee requirements: power output, net specific heat rate,
auxiliary power consumption, and NOx emission level. These are heavily
qualified by a set of correction curves that relate to the various differences
between reference conditions and those experienced at the installation site.
The main ones are:
• governing characteristics;
• overspeed settings;
• vibration and critical speeds;
• noise levels.
Specifications and standards
The following standards are in common use in the GT industry.
• ISO 3977: (1991) Guide for gas turbine procurement, identical to BS
3863: 1992. This is a guidance document, useful for information on
definitions of cycle parameters and for explaining different open and
closed cycle arrangements.
• ISO 2314 Gas turbine acceptance tests, identical to BS 3135. This is not
a step-by-step procedure for carrying out a no-load running test, but
contains mainly technical information on parameter variations and
measurement techniques for pressures, flows, powers, etc.
• ANSI/ASME PTC 22 Gas turbine power plants. This is one of the power
test codes (PTC) family of standards. Its content is quite limited, covering
broadly the same area as ISO 2314, but in less detail.
Prime Movers 241
Journal and thrust bearing compressor end
Journal bearing turbine end
Fig. 9.21 GT shaft bearings
Engineers’ Guide to Rotating Equipment242
• API 616 Gas turbines for refinery service. In the mould of most API
standards, this provides good technical coverage. There is a bit of
everything to do with gas turbines.
• ISO 1940/1: (1986) Balance quality requirements of rigid rotors. Part I –
Method for determination of possible residual inbalance (identical to BS
6861 Part 1 and VDI 2060) covers balancing of the rotor. It gives
acceptable unbalance limits.
• ISO 10494: (1993) Gas turbines and gas turbine sets; measurement of
emitted airborne noise – engineering survey method (similar to BS 7721)
and ISO 1996 are standards relating to GT noise levels.
Vibration standards
• Bearing housing vibration is covered by VDI 2056 (group T). This is a
commonly used standard for all rotating machines. It uses vibration
velocity (mm/s) as the deciding parameter.
• Shaft vibrations using direct-mounted probes are covered by API 616 or
ISO 7919/1 (also commonly used for other machines). The measured
vibration parameter is amplitude. VDI 2059 (Part 4) is sometimes used,
but it is a more theoretical document that considers the concept of non-
sinusoidal vibrations.
Bearing vibration and
movement sensor
Bearing temperature
sensors
Fig. 9.22 GT bearing sensors
Prime Movers 243
Rotor runout measurement
The measured parameter is Total Indicated Runout (TIR). This is the
biggest recorded difference in dial test indicator (d.t.i.) reading as the rotor
is turned through a complete revolution. Figure 9.23 shows a typical results
format.
• Acceptance limits. The maximum acceptable TIR is usually defined by
the manufacturer rather than specified directly by a technical standard.
The tightest limit is for the bearing journals (typically 10–15 µm). Radial
surfaces of the turbine blade discs should have a limit of 40–50 µm. Axial
faces of the discs often have a larger limit, perhaps 70–90 µm. The exact
limits used depend on the design.
Fig. 9.23 GT rotor runout measurement
Engineers’ Guide to Rotating Equipment244
Rotor dynamic balancing
Gas turbine rotors are all subjected to dynamic balancing, normally with all
the blades installed. Procedures can differ slightly; turbines that have separate
compressor and turbine shafts may have these balanced separately (this is
common on larger three-bearing designs) although some manufacturers prefer
to balance the complete rotor assembly. The important parameter is the limit
of acceptable unbalance expressed per correction plane (as in ISO 1940) in
gramme metres (g.m). Figure 9.24 shows the arrangement.
Fig. 9.24 Two-plane (dynamic) balancing of a GT rotor
Rotor overspeed test
Gas turbine rotors are subjected to an overspeed test with all the compressor
and turbine blades in position. The purpose is to verify the mechanical
integrity of the stressed components without stresses reaching the elastic
limit of the material. It also acts as a check on vibration characteristics at the
rated and overspeed condition. The test consists of running the rotor at 120
per cent rated speed for three minutes. Drive is by a large electric motor and
the test is performed in a concrete vacuum chamber to eliminate windage.
Full vibration monitoring to VDI 2056 or API 616 is performed, as
mentioned earlier.
Prime Movers 245
Blade clearance checks
The purpose is to verify running clearances between the ends of the rotor
blades and the inside of the casing. Clearances that are too large will result
in reduced stage efficiency. If the clearances are too tight, the blades may
touch the inside of the casing and cause breakage, particularly at the
compressor end. Figure 9.25 shows the arrangement. Indicative clearances
(measured using slip gauges) are:
• compressor end stage 1–5 – 1.6 to 2.0 mm
• compressor end stage 9–16 – 1.8 to 2.4 mm
• compressor end stage 16+ – 2.0 to 2.4 mm
• turbine end – 4.0 to 4.5 mm
• rotor axial position (end – 7.0 to 8.0 mm
clearance of last blades)
Figure 9.26 shows the profile of the GT no-load running test.
Noise measurement
Most contract specifications require that the GT be subject to a noise
measurement check. The main technical standard relating to GT noise
testing is ISO 10494: (1993) Measurement of airborne noise (equivalent to
BS 7721). This is referred to by the GT procurement standard ISO 3977 and
contains specific information about measuring GT noise levels. Noise
measurement principles and techniques are common for many types of
engineering equipment, so the following general technical explanations can
be applied equally to diesel engines, gearboxes, or pumps.
Principles
It is easiest to think of noise as airborne pressure pulses set up by a vibrating
surface source. It is measured by an instrument that detects these pressure
changes in the air and then relates this measured sound pressure to an
accepted ‘zero’ level. Because a machine produces a mixture of frequencies
(termed ‘broad-band’ noise), there is no single noise measurement that will
describe fully a noise emission. Two measurements are normally taken:
• The ‘overall noise’ level This is a colloquial term for what is properly
described as the ‘A-weighted sound pressure level’. It incorporates
multiple frequencies and weights them according to a formula which
results in the best approximation of the loudness of the noise. This is
displayed as a single instrument reading expressed as decibels – in this
case dB(A).
Engineers’ Guide to Rotating Equipment246
Fig. 9.25 GT clearance checks
Prime Movers 247
Fig. 9.26 GT no-load run test
• ‘Frequency band’sound pressure level This involves measuring the sound
pressure level in a number of frequency bands. These are arranged in
either octave or one-third octave bands in terms of their mid-band
frequency. The frequency range of interest in measuring machinery noise
is from about 30 Hz to 10 000 Hz.
GT noise characteristics
Gas turbines produce a wide variety of broad-band noise across the
frequency range. There are three main emitters of noise: the machine’s total
surface, the air inlet system, and the exhaust gas outlet system. In practice,
the inlet and outlet system noise is considered as included in the surface-
originated noise. The machine bearings emit noise at frequencies related
to their rotational speed, while the combustion process emits a wider,
less predictable range of sound frequencies. Many industrial turbines
are installed within an acoustic enclosure to reduce the levels of ‘near
vicinity’ and environmental (further away) noise. Figure 9.27 shows the test
arrangement.
Engineers’ Guide to Rotating Equipment248
Fig. 9.27 GT noise tests
Prime Movers 249
9.4 Gearboxes and testingAs precision items of rotating equipment, gearboxes are subject to various
checks and tests during manufacture. The main checks during a test of a
large spur, helical, or epicyclic gearbox are for:
• a correctly machined and aligned gear train;
• correctly balanced rotating parts;
• mechanical integrity of the components, particularly of the highly stressed
rotating parts and their gear teeth.
Table 9.5 shows a typical acceptance guarantee schedule for a large gearbox.
Table 9.5 Large gearbox – typical acceptance
guarantee schedule
The design standard e.g. API 613
Rated input/output speeds 5200/3000 r/min
Overspeed capability 110 per cent (3300 r/min)
No-load power losses Maximum 510 kW (this is sometimes expressed
as a percentage value of the input power)
Oil flow 750 l/min (with a tolerance of ± 5 per cent)
Casing vibration VDI 2056 group T: 2.8 mm/s r.m.s. (measured
as a velocity)
Shaft vibration Input pinion 39 µm
Output shaft 50 µm peak-to-peak (both
measured as an amplitude)
Noise level ISO 3746: 97 dB(A) at 1 m distance
Gear inspection standards
Gear design and inspection standards are defined at the specification stage
and relate to the application of the gearbox. Some commonly used ones are:
• API 613: (1988) Special service gear units for refinery service. This has
direct relevance to works inspection and is used in many industries. For
further technical details, API 613 cross-references the American Gear
Manufacturers Association (AGMA) range of standards.
• VDI 2056: (1984) covers criteria for assessing mechanical vibration of
machines. It is only applicable to the vibration of gearbox bearing
housings and casings, not the shafts. Machinery is divided into six
application ‘groups’ with gearboxes clearly defined as included in group
Engineers’ Guide to Rotating Equipment250
T. Vibration velocity (r.m.s.) is the measured parameter. Acceptance
levels are clearly identified.
• ISO 2372: (1988) (equivalent to BS 4675) covers a similar scope to VDI
2056 but takes a different technical approach.
• ISO 8579: (1992) (equivalent to BS 7676) is in two parts, covering noise
and vibration levels. It provides good coverage, but is not in such
common use as other ISO and VDI standards.
• ISO 7919/1: (1986) (equivalent to BS 6749 Part 1). This relates
specifically to the technique of measuring shaft vibration.
• ISO 3746 and API 615 are relevant noise standards. Other parts of test
procedures addressed by standards are dynamic balancing and tooth
contact tests.
Dynamic balancing test
Dynamic balancing is normally carried out after assembly of the gear wheels
and pinions to their respective shafts. The rotor is spun at up to its rated
speed and multiphase sensors, mounted in the bearings housings, sense the
unbalance forces, relaying the values to a suitable instrument display. The
purpose of dynamic balancing is to reduce the residual unbalance to a level
which will ensure that the vibration characteristics of the assembled gearbox
are acceptable. There is a useful first approximation for maximum
permissible unbalance in API 613 (see Fig. 9.28). The correct compound
unit is g.mm (gramme millimetres), i.e. an unbalance mass operating at an
effective radius from the rotational axis. Any residual unbalance is corrected
(after stopping the rotor) by adding weights into threaded holes. The test is
then repeated to check the results.
Contact checks
Contact checks are a simple method of checking the meshing of a gear train.
The results provide information about the machined accuracy of the gear
teeth, and the relative alignment of the shafts. The test consists of applying
a layer of ‘engineers’ blue’ colour transfer compound to the teeth of one gear
of each meshing set and then rotating the gears in mesh. The colour transfer
shows the pattern of contact across each gear tooth (see Fig. 9.29).
Running tests
The mechanical running test is the key proving step for the gearbox. Most
purchasers rely on a no-load running test, also referred to as a ‘proof test’.
The key objectives of the mechanical running test are to check that the oil
flows, and that vibration and noise levels produced by the gearbox are
Prime Movers 251
Fig. 9.28 Dynamic balance of a gear rotor
Engineers’ Guide to Rotating Equipment252
Fig. 9.29 Gear train contact checks
Prime Movers 253
within the guarantee acceptance levels. The test procedure contains the
following steps (see Figs 9.30 and 9.31):
• slow-speed run
• run-up
• rated speed run
• overspeed test
• noise measurements
• stripdown.
Fig. 9.30 Gearbox no-load running test
Engineers’ Guide to Rotating Equipment254
Fig. 9.31 Gearbox running test – monitoring
Prime Movers 255
9.5 Reciprocating internal combustion
enginesInternal combustion (IC) engines are classified basically into spark ignition
(petrol) engines and compression ignition (diesel) engines. Petrol engines
are used mainly for road vehicles up to a power of about 400 kW, while
diesel engines, in addition to their use in road vehicles, are used in larger
sizes for power generation, and locomotive and marine propulsion.
Diesel engines
Diesel engines are broadly divided into three categories based on speed.
Table 9.6 gives a guide.
Table 9.6 Diesel engine speed categories
Designation Application (Brake) R/min Piston speed
Power rating (m/s)
(MW)
Slow speed Power generation, Up to 45 <150 <9
(2 or 4 stroke) ship propulsion
Medium speed Power generation, Up to 15 200–800 <12
(4 stroke) ship propulsion
High speed Locomotives, Up to 5 >800 12–17
(4 stroke ‘V’) portable power
generation
Diesel engine performance
Engine performance is the main issue that drives the ongoing design and
development of diesel engines. The prime performance criterion is ‘specific’
fuel consumption (s.f.c.). Expressed in grammes (of fuel) per brake power
(kW) hour, this is a direct way of assessing and comparing engines.
Engine guarantee schedules follow the pattern shown in Table 9.7, which
shows indicative parameters for a medium-speed engine. Some key design
requirements such as critical speed range, governor characteristics,
acceptable bearing temperatures, and peak cylinder pressures are not stated
explicitly, but do form part of an overall performance assessment of an
engine. Figure 9.32 shows details of the brake test carried out to assess
compliance with specified performance guarantees.
Engineers’ Guide to Rotating Equipment256
Table 9.7 Typical diesel engine guarantee schedule
Prime Movers 257
Fig. 9.32 Diesel engine brake test
Engineers’ Guide to Rotating Equipment258
Crankshaft deflections
Crankshaft deflection measurements are a way of checking crankshaft and
bearing alignment. Figure 9.33 shows the basic methodology.
Fig. 9.33 Crankshaft web deflections
Prime Movers 259
Diesel engine technical standards
The main body of technical standards for diesel engines are those relating to
testing of the engine. The most commonly used is ISO 3046: Parts 1 to 7
Reciprocating internal combustion engines: performance, identical in all
respects to BS 5514 Parts 1 to 7.
• ISO 3046/1 Standard reference conditions defines the standard ‘ISO’
reference conditions that qualify engine performance.
• ISO 3046/2 Test methods describes the principles of acceptance
guarantees during the load (brake) test and explains how to relate engine
power at actual test conditions to ISO conditions and site conditions (both
of which normally feature in the engine’s guarantee specification).
• ISO 3046/3 Test measurements gives permissible deviations for test
temperatures and pressures.
• ISO 3046/4 Speed governing defines the five possible classes of
governing accuracy. An engine specification and acceptance guarantee
will quote one of these classes.
• ISO 3046/5 Torsional vibrations is a complex technical part of the
standard and covers the principles of torsional vibration as applied
specifically to reciprocating engines.
• ISO 3046/6 Specification of overspeed protection defines the overspeed
levels.
• ISO 3046/7 Codes for engine power defines the way that manufacturers
frequently classify the power output of their range of engines using a
string of code numbers.
Table 9.8 shows some other related technical standards.
Engineers’ Guide to Rotating Equipment260
Table 9.8 Technical standards – IC engines
9.6 TurbochargersMost modern diesel engines, and many petrol engines, are fitted with
turbochargers. Because of their high speed, turbochargers are a highly
complex and precision item of rotating equipment. Sizes range from large
units fitted to marine diesel engines down to those used on motor vehicle
engines. The smaller variants develop very quickly, as designs adapt to
onerous conditions of speed, temperature, and fluid flow.
Standard Title Status
BS AU 141a: 1971 Specification for the performance of
diesel engines for road vehicles.
Current
BS ISO 2697: 1999 Diesel engines. Fuel nozzles. Size
'S'.
Current
BS ISO 4093: 1999 Diesel engines. Fuel injection pumps.
High-pressure pipes for testing.
Current
BS ISO 7299: 1996 Diesel engines. End-mounting
flanges for fuel injection pumps.
Current
BS ISO 7612: 1994 Diesel engines. Base-mounted in-line
fuel injection pumps. Mounting
dimensions.
Current
BS EN ISO 8178-4:
1996
Reciprocating internal combustion
engines. Exhaust emission
measurement. Test cycles for
different engine applications.
Current
BS EN ISO 8178-5:
1997
Reciprocating internal combustion
engines. Exhaust emission
measurement. Test fuels.
Current
BS ISO 14681: 1998 Diesel engines. Fuel injection pump
testing. Calibrating fuel injectors.
Current
BS EN 1679 1: 1998 Reciprocating internal combustion
engines. Safety. Compression
ignition engines.
Current
96/714952 Reciprocating internal combustion
engines. Performance. Part 4.
Speed governing.
Current, draft
for public
comment
Prime Movers 261
Principles of turbocharger operation
Figure 9.34 shows a small diesel engine turbocharger design. The exhaust
gases of the engine are expanded in the tangential volute of the uncooled
turbine casing and fed to a turbine rotor. Owing to the design of the volute,
the gases are accelerated with a minimal loss of energy, so that the highest
possible efficiency is attained. The turbine rotor drives the compressor
impeller through the rotor shaft. The air to be compressed enters via a
filter/silencer arrangement. After compression, the air is then fed to the
engine inlet. A system of journal and roller bearings support the shaft, which
rotates at high speed.
Turbochargers suffer from ‘lag’, a condition under which very little
‘boost’ air pressure is produced, owing to low exhaust gas volume flow
when the engine is running at low speed. The overall design performance of
a turbocharger is essentially controlled by three parameters: the type of
exhaust turbine, the geometry ratio of the exhaust housing, and the geometry
of the compressor.
Housings
Inducer
region
Exducer
region
Scalloped
disc between
vanes
Vaneless
diffuser region
Fig. 9.34 Small turbocharger design
Engineers’ Guide to Rotating Equipment262
Exhaust turbine
Exhaust turbine design is a balance between absorbing as much energy from
the exhaust gases as possible, and allowing the gases to flow as easily as
possible. This is closely related to the size of the exhaust housing. A larger
turbine can absorb more energy from the gases and spin the shaft with more
torque and speed, but too large a turbine will restrict the flow of exhaust,
thereby reducing engine performance.
Turbine housings geometry
Exhaust gas flow can be improved by incorporating design features such as
nozzles or ‘scrolls’ that direct the exhaust gas flow directly onto the turbine
blades. Such features affect the rate at which the turbine will accelerate, but
these must be balanced against restricting the flow areas too much, since this
will cause flow restrictions and increase undesirable backpressure on the
engine, thereby reducing performance.
Compressor geometry
A turbocharger compressor housing is designed to convert the kinetic energy
of the air into pressure energy. The size of the compressor turbine
determines the maximum amount of air pressure ‘boost’ that the
turbocharger can produce as well as its acceleration characteristic. In small
engines the amount of boost produced is controlled by a ‘wastegate’. The
wastegate is a vacuum- or solenoid-actuated valve located at the exhaust
inlet to the turbo which, when opened, causes the exhaust gases to bypass
the exhaust turbine instead of passing through it. The further the wastegate
is opened, the more exhaust is bypassed and the less boost is produced.
Some designs also have a blow-off valve on the discharge manifold of the
turbocharger casing. This is a vacuum-actuated valve that opens when there
is vacuum in the intake manifold (closed-throttle). The release in pressure
slows the run-down time of the turbocharger rotor and avoids undesirable
pressure fluctuations.
CHAPTER 10
Draught Plant
10.1 AeropropellersA propeller, or ‘airscrew’, converts the torque of an engine (piston engine or
turboprop) into thrust. Propeller blades have an airfoil section that becomes
more ‘circular’ towards the hub. The torque of a rotating propeller imparts
a rotational motion to the air flowing through it. Pressure is reduced in front
of the blades and increased behind them, creating a rotating slipstream.
Large masses of air pass through the propeller, but the velocity rise is small
compared to that in turbojet and turbofan engines.
Blade element design theory
Basic design theory considers each section of the propeller as a rotating
airfoil. The flow over the blade is assumed to be two dimensional (i.e. no
radial component). From Fig. 10.1 the following equations can be expressed
Pitch angle φ = tan–1 (Vo/πnd)
u = velocity of blade element = 2πnr
The propulsion efficiency (ηb) of the blade element, i.e. the ‘blading
efficiency’, is defined by
ob
d tan / tan
d tan( ) / cot
V F L D
u Q L D
φ φηφ γ φ
−= = =+ +
Engineers’ Guide to Rotating Equipment264
where
D = drag
L = lift
dF = thrust force acting on blade element
dQ = corresponding torque force
r = radius
The value of φ that makes ηb a maximum is termed the ‘optimum advance
angle’ φopt.
Fig. 10.1 Aeropropeller design
α
α
Draught Plant 265
Maximum blade efficiency is given by
Performance characteristics
The pitch and angle φ have different values at different radii along a
propeller blade. It is common to refer to all parameters determining the
overall characteristics of a propeller to their values at either 0.7r or 0.75r.
Lift coefficient CL is a linear function of the angle of attack α up to the
point where the blade stalls, while drag coefficient CD is a quadratic function
of α. Figure 10.2 shows broad relationships between blading efficiency,
pitch angle, and L/D ratio.
b max
2 1 2( / ) 1( )
2 1 2( / ) 1
L D
L D
γηγ
− −= =+ +
Fig. 10.2 A square key end shape
Propeller coefficients
It can be shown, neglecting the compressibility of the air, that
f(Vo, n, dp, ρ, F) = 0
Using dimensional analysis, the following coefficients are obtained for
expressing the performances of propellers having the same geometry
F = ρn2d 4pCF Q = ρn2d 5pCQ P = ρn3d 5
pCp
CF, CQ, and CP are termed the thrust, torque, and power coefficients. These
Engineers’ Guide to Rotating Equipment266
are normally expressed in USCS units
Thrust coefficient CF
Torque coefficient CQ
Power coefficient CP
where
d = propeller diameter (ft)
n = speed in revs/s
Q = torque (ft.lbs)
F = thrust (lbf)
P = power (ft.lbs/s)
ρ = air density (lb.s2/ft4)
Activity factor
Activity factor (AF) is a measure of the power-absorbing capabilities of a
propeller, and hence a measure of its ‘solidity’. It is defined as
Propeller mechanical design
Propeller blades are subjected to:
• tensile stress due to centrifugal forces;
• steady bending stress due to thrust and torque forces;
• bending stress caused by vibration.
Vibration-induced stresses are the most serious, so propellers are designed
so that their first-order, natural resonant frequency lies above expected
operating speeds. To minimize the chance of failures, blades are designed
using fatigue strength criteria. Steel blades are often hollow, whereas
aluminium alloy ones are normally solid.
2 4
F
n dρ=
2 5
Q
n dρ=
3 4
P
n dρ=
3/ 1
/P
100 000AF
16
r R
r Rh
c r rd
d R R
= = ∫
Draught Plant 267
10.2 Draught fansThere are two main types of fan: axial and centrifugal. Axial fans are mainly
used in low-pressure applications, making the centrifugal type the most
common design. Figure 10.3 shows a typical large centrifugal fan.
Fig. 10.3 Centrifugal draught fan – general view
Engineers’ Guide to Rotating Equipment268
Figure 10.4 shows a typical fan operating characteristic. Note how the
characteristic reflects the amount of pressure it takes to push air through the
system. Inlet control vanes are often used to help locate the operating point.
The system resistance line shows how the fan efficiency reduces as the air
flow and pressure decrease. An alternative method of control is by using
variable speed drive motors or variable speed hydraulic couplings.
Fig. 10.4 Centrifugal fan – typical operating characteristic
Stall conditions
Every fan has a stable and unstable operating range. Stable flow is defined
as the condition under which enough air flows through the fan wheel to
provide a constant static pressure output for a given flow. As pressure is
increased and flow reduced, the fan follows the curve to the left of the
original operating point. At some point, the airflow is reduced to a point
where individual fan blades, and then all the blades, enter a stalled
condition, causing the flow regime to break down.
Draught Plant 269
Critical speeds
Operation of a fan too near its critical speed will make it very sensitive to
out-of-balance forces and resulting vibration. As a rule of thumb, the normal
operating speed of a fan should be at least 20 per cent below the first critical
speed.
Useful standards
Table 10.1 shows some published technical standards relating to draught
fans and similar equipment.
Table 10.1 Technical standards – fans
Standard Title Status
BS 848-1: 1997,
ISO 5801: 1997
Fans for general purposes.
Performance testing using standardized
airways.
Current
BS 848-2: 1985 Fans for general purposes. Methods of
noise testing.
Current,
partially
replaced
BS 848-4: 1997,
ISO 13351: 1996
Fans for general purposes. Dimensions. Current
BS 848-5: 1999,
ISO 12499: 1999
Fans for general purposes. Special for
mechanical safety (guarding).
Current
BS 848-6: 1989 Fans for general purposes. Method of
measurement of fan vibration.
Current, work
in hand
BS 848-8: 1999,
ISO 13349: 1999
Fans for general purposes. Vocabulary
and definition of categories.
Current
BS 848-10: 1999,
ISO 13350: 1999
Fans for general purposes.
Performance testing of jet fans.
Current
BS 5060: 1987,
IEC 60879: 1986
Specification for performance and
construction of electric circulating fans
and regulators.
Current,
confirmed
BS EN 25136:
1994,
ISO 5136: 1990
Acoustics. Determination of sound
power radiated into a duct by fans.
In-duct method.
Current, work
in hand
BS EN 45510-4-3:
1999
Guide for the procurement of power
station equipment. Boiler auxiliaries.
Draught plant.
Current
88/72307 DC General purpose industrial fans. Fan
size designation (ISO/DIS 8171).
Current, draft
for public
comment
Engineers’ Guide to Rotating Equipment270
10.3 ‘Fin-fan’ coolersAir-cooled, tube-nest heat exchangers (known loosely as ‘fin-fan’ coolers)
are in common use for primary cooling purposes in desert areas or in inland
plant sites. On a smaller scale, they have multiple uses in chemical and
process plants where a self-contained cooling unit is needed, avoiding the
complication of connecting every heat ‘sink’ component to a centralized
cooling circuit. In their larger sizes, fin-fan coolers can cover an area of up
to 4000–5000 m2 and often stand up in a shallow angle ‘A’ configuration.
Smaller ones usually stand horizontally, resting on a simple structural steel
frame.
Construction
Figure 10.5 shows a basic fin-fan cooler design; they vary very little
between manufacturers. The main design points are outlined below.
89/76909 DC BS 848. Part 8. Fan terminology and
classification.
Current, draft
for public
comment
95/704659 DC Machines for underground mines.
Safety requirements for mining
ventilation machinery. Electrically driven
fans for underground use (prEN 1872).
Current, draft
for public
comment
97/719334 DC Ventilation for buildings. Air handling
units. Ratings and performance for
components and sections (prEN
13053).
Current, draft
for public
comment
98/704585 DC Ventilation for buildings. Performance
testing of components/products for
residential ventilation. Part 4. Fans used
in residential ventilation systems (prEN
13141-4).
Current, draft
for public
comment
98/718875 DC Industrial fans. Performance testing in
situ (ISO/DIS 5802).
Current, draft
for public
comment
00/561592 DC Acoustics. Determination of sound
power radiated into a duct by fans and
other air-moving devices. In-duct
method (ISO/DIS 5136).
Current, draft
for public
comment
00/704961 DC ISO/DIS 14694. Industrial fans.
Specification for balance quality and
vibration levels.
Current, draft
for public
comment
Table 10.1 Cont.
Draught Plant 271
Fig. 10.5 ‘Fin-fan’ cooler fan – general arrangement
Engineers’ Guide to Rotating Equipment272
The cooling matrix
This consists of a matrix of extruded carbon steel or stainless steel finned
tubes arranged in a complex multi-pass flow path. The matrix is often
divided into discrete banks of tubes, extending horizontally between a set of
headers. The fins consist of a continuous spiral-wound, thin steel strip that
is resistance-welded into a thin slot machined in a close helix around the
tubes’ outer surface. The extended surface of the fins adds significantly to
the effective surface area, thereby increasing the overall thermal transfer. A
typical tube bank is between six and ten tubes ‘deep’ in order to achieve the
necessary heat transfer in as small a (horizontal) area as possible.
The headers
Each end of the tube banks are stub-welded into heavy-section cast and
welded headers. These contain internal division plates and baffles that give
the desired multi-pass pattern through the system. Each header also contains
stub pieces and small access hatches for inspection, cleaning, and bleeding
off unwanted air during commissioning. In most designs, the headers are
designed and built to an accepted pressure vessel standard.
The air fans
Primary cooling effect is provided by a bank of axial-flow cooling fans that
blow air vertically upwards through the tube nest. Fans are generally belt-
driven for simplicity, and have variable incidence blades positioned by a
pneumatic actuator arrangement. The electric motors are often two-speed
(typically 300 r/min and 600 r/min), to allow operating current and power
consumption to be reduced when air temperature is low. In a typical unit,
each fan will be located about 2 m off the ground and will be protected by
an expanded metal safety guard. Tip speed of the fan is normally kept below
60 m/s to avoid over-stressing the aluminium blades.
Fan running testing procedures
Fans are normally tested with their ‘contract’ motor – ‘shop test’ motors do
not allow a proper assessment of the running current that will be
experienced after site installation. Figure 10.6 shows a section through a
typical fan, the shape of its performance characteristic, and the main points
to check. The running test does not normally follow any particular technical
standard; rather, it is organized around the task of demonstrating the fan’s
fitness-for-purpose in use. Specific points are as follows:
Draught Plant 273
• Static pressure versus blade angle The performance of the fan does not
keep on improving as blade incidence is increased. There is a well-
defined ‘cut-off point’, above which the blades start to become
aerodynamically inefficient and will actually produce less, rather than
more, cooling effect.
• Blade angle versus motor current This places a limitation on the fitness-
for-purpose of the fan. Maximum motor design currents usually have a
design margin of about 30 per cent (to keep the cost of the motors down).
A well-designed unit should reach full operating current before the static
pressure curve levels off.
• Vibration Axial fans are normally smooth-running units and rarely
experience vibration problems. A maximum Vrms level of about 2.5 mm/s
is acceptable, using the principles of VDI 2056.
• Mechanical integrity: points to check
– blade locking arrangements, including the fitted ‘clevis’, used to locate
the blades accurately in position on the hub;
– the pneumatic positioner and diaphragm that move the blade angle;
– the blades themselves (usually aluminium): check for length and any
obvious mechanical damage;
– all locknuts and lockwashers fitted to the rotating components.
Engineers’ Guide to Rotating Equipment274
Fig. 10.6 ‘Fin-fan’ cooler fan – typical performance
characteristics
CHAPTER 11
Basic Mechanical Design
11.1 Engineering abbreviationsTable 11.1 shows abbreviations that are in common use in engineering
drawings and specifications for rotating equipment.
Table 11.1 Engineering abbreviations
Abbreviation Meaning
A/F Across flats
ASSY Assembly
CRS Centres
L or CL Centre line
CHAM Chamfered
CSK Countersunk
C’BORE Counterbore
CYL Cylinder or cylindrical
DIA Diameter (in a note)
∅ Diameter (preceding a dimension)
DRG Drawing
EXT External
FIG. Figure
HEX Hexagon
INT Internal
LH Left hand
LG Long
MATL Material
Engineers’ Guide to Rotating Equipment276
MAX Maximum
MIN Minimum
NO. Number
PATT NO. Pattern number
PCD Pitch circle diameter
RAD Radius (in a note)
R Radius (preceding a dimension)
REQD Required
RH Right hand
SCR Screwed
SH Sheet
SK Sketch
SPEC Specification
SQ Square (in a note)
Square (preceding a dimension)
STD Standard
VOL Volume
WT Weight
11.2 American terminologyIn the USA, slightly different terminology is used, see Table 11.2. These
abbreviations are based on the published standard ANSI/ASME Y14.5:
(1994) Dimensioning and tolerancing.
Table 11.2 American abbreviations
Abbreviation Meaning
ANSI American National Standards Institute
ASA American Standards Association
ASME American Society of Mechanical Engineers
AVG Average
CBORE Counterbore
CDRILL Counterdrill
CL Centre line
CSK Countersink
Table 11.1 Cont.
Basic Mechanical Design 277
FIM Full indicator movement
FIR Full indicator reading
GD&T Geometric dimensioning and tolerancing
ISO International Standards Organisation
LMC Least material condition
MAX Maximum
MDD Master dimension definition
MDS Master dimension surface
MIN Minimum
mm Millimetre
MMC Maximum material condition
PORM Plus or minus
R Radius
REF Reference
REQD Required
RFS Regardless of feature size
SEP REQT Separate requirement
SI Système International (the metric system)
SR Spherical radius
SURF Surface
THRU Through
TIR Total indicator reading
TOL Tolerance
11.3 Preferred numbers and preferred sizesPreferred numbers are derived from geometric series in which each term is
a uniform percentage larger than its predecessor. The first five principal
series (named the ‘R’ series) are shown in Table 11.3.
Preferred numbers are taken as the basis for ranges of linear sizes of
components, often being rounded up or down for convenience. Figure 11.1
shows the development of the R5 and R10 series.
Table 11.2 Cont.
Engineers’ Guide to Rotating Equipment278
Table 11.3 Preferred number series
Series Basis Ratio of terms
(% increase)
R5 5√10 1.58 (58%)
R10 10√10 1.26 (26%)
R20 20√10 1.12 (12%)
R40 40√10 1.06 (6%)
R80 80√10 1.03 (3%)
Fig. 11.1 The R5 and R10 series
Useful references
BS 2045: (1982) Preferred numbers. Equivalent to ISO 3.
11.4 Datums and tolerances – principlesA ‘datum’ is a reference point or surface from which all other dimensions of
a component are taken; these other dimensions are said to be ‘referred to’
the datum. In most practical designs, a datum surface is usually used, this
generally being one of the surfaces of the machine element itself rather than
an ‘imaginary’ surface. This means that the datum surface normally plays an
important part in the operation of the elements. The datum surface is usually
machined and may be a mating surface or a locating face between elements,
or similar (see Figs 11.2 and 11.3). Simple machine mechanisms do not
always need datums – it depends on what the elements do and how
complicated the mechanism assembly is.
A ‘tolerance’ is the allowable variation of a linear or angular dimension
about its ‘perfect’ value. British Standard 308 and similar published
standards contain accepted methods and symbols.
Basic Mechanical Design 279
Toleranced dimensions
In designing any engineering component it is necessary to decide which
dimensions will be toleranced. This is predominantly an exercise in
necessity – only those dimensions that must be tightly controlled, to
preserve the functionality of the component, should be toleranced (see
Fig. 11.4). Too many toleranced dimensions will increase significantly the
manufacturing costs and may result in ‘tolerance clash’, where a dimension
derived from other toleranced dimensions can have several contradictory
values.
Fig. 11.2 Datums and tolerances
Fig. 11.3 The tolerance frame
Engineers’ Guide to Rotating Equipment280
General tolerances
It is a sound principle of engineering practice that in any rotating machine
design there will only be a small number of toleranced features. The
remainder of the dimensions will not be critical.
There are two ways to deal with this. First, an engineering drawing or
sketch can be annotated to specify that a ‘general tolerance’ should apply to
features where no specific tolerance is mentioned. This is often expressed as
± 0.5 mm. Alternatively, the drawing can make reference to a ‘general
tolerance’ standard such as BS EN 22768, which gives typical tolerances for
linear dimensions, as shown in Table 11.4.
Table 11.4 Typical tolerances for linear dimensions
Dimension (mm) Tolerance (mm)
0.6–6.0 ± 0.1
6–36 ± 0.2
36–120 ± 0.3
120–315 ± 0.5
315–1000 ± 0.8
Fig. 11.4 Toleranced dimensions
Basic Mechanical Design 281
11.5 HolesThe tolerancing of holes depends on whether they are made in thin sheet (up
to about 3 mm thick) or in thicker plate material. In thin material, only two
toleranced dimensions are required (see Fig. 11.5).
• Size A toleranced diameter of the hole, showing the maximum and
minimum allowable dimensions.
• Position Position can be located with reference to a datum and/or its
spacing from an adjacent hole. Holes are generally spaced by reference to
their centres.
Fig. 11.5 Tolerances – holes
For thicker material, three further toleranced dimensions become relevant:
straightness, parallelism, and squareness.
• Straightness A hole or shaft can be straight without being perpendicular to
the surface of the material.
• Parallelism This is particularly relevant to holes and is important when
there is mating hole-to-shaft fit.
• Squareness The formal term for this is ‘perpendicularity’. Simplistically,
it refers to the squareness of the axis of a hole to the datum surface of the
material through which the hole is made.
Engineers’ Guide to Rotating Equipment282
11.6 Screw threadsThere is a well-established system of tolerancing adopted by British and
International Standard Organizations and the manufacturing industry. This
system uses the two complementary elements of fundamental deviation and
tolerance range to define fully the tolerance of a single component. It can be
applied easily to components, such as screw threads, which join or mate
together (see Fig. 11.6).
• Fundamental deviation (FD) is the distance (or ‘deviation’) of the nearest
‘end’ of the tolerance band from the nominal or ‘basic’ size of a
dimension.
• Tolerance band (or ‘range’) is the size of the tolerance band, i.e. the
difference between the maximum and minimum acceptable size of a
toleranced dimension. The size of the tolerance band, and the location of
the FD, governs the system of limits and fits applied to mating parts.
Fig. 11.6 Tolerances – screw threads
Basic Mechanical Design 283
Tolerance values have a key influence on the costs of a manufactured item,
so their choice must be seen in terms of economics as well as engineering
practicality. Mass-produced items are competitive and price sensitive, and
over-tolerancing can affect the economics of a product range.
11.7 Limits and fits
Principles
In machine element design there is a variety of different ways in which a
shaft and hole are required to fit together. Elements such as bearings,
location pins, pegs, spindles, and axles are typical examples. The shaft may
be required to be a tight fit in the hole, or to be looser, giving a clearance to
allow easy removal or rotation. The system designed to establish a series of
useful fits between shafts and holes is termed ‘limits and fits’. This involves
a series of tolerance grades so that machine elements can be made with the
correct degree of accuracy and can be interchangeable with others of the
same tolerance grade (see Fig. 11.7).
The British Standard BS 4500/BS EN 20286 ISO Limits and fits contains
the recommended tolerances for a wide range of engineering requirements.
Each tolerance grade is designated by a combination of letters and numbers,
such as IT7, which would be referred to as grade 7.
Fig. 11.7 Limits and fits
Engineers’ Guide to Rotating Equipment284
Figure 11.7 shows the principles of a shaft/hole fit. The ‘zero line’ indicates
the basic or ‘nominal’ size of the hole and shaft (it is the same for each) and
the two shaded areas depict the tolerance zones within which the hole and
shaft may vary. The hole is conventionally shown above the zero line. The
algebraic difference between the basic size of a shaft or hole and its actual
size is known as the ‘deviation’.
• It is the deviation that determines the nature of the fit between a hole and
a shaft.
• If the deviation is small, the tolerance range will be near the basic size,
giving a tight fit.
• A large deviation gives a loose fit.
Various grades of deviation are designated by letters, similar to the system
of numbers used for the tolerance ranges. Shaft deviations are denoted by
small letters, and hole deviations by capital letters. Most general
engineering uses a ‘hole-based’ fit in which the larger part of the available
tolerance is allocated to the hole (because it is more difficult to make an
accurate hole) and then the shaft is made to suit, to achieve the desired fit.
Common combinations
There are seven popular combinations used in general mechanical
engineering design (see Fig. 11.8).
1. Easy running fit: H11–c11, H9–d10, H9–e9. These are used for bearings
where a significant clearance is necessary.
2. Close running fit: H8–f7, H8–g6. This only allows a small clearance,
suitable for sliding spigot fits and infrequently used journal bearings.
This fit is not suitable for continuously rotating bearings.
3. Sliding fit: H7–h6. Normally used as a locational fit in which close-fitting
items slide together. It incorporates a very small clearance and can still be
freely assembled and disassembled.
4. Push fit: H7–k6. This is a transition fit, mid-way between fits that have a
guaranteed clearance and those where there is metal interference. It is
used where accurate location is required, e.g. dowel and bearing inner-
race fixings.
5. Drive fit: H7–n6. This is a tighter grade of transition fit than the H7–k6.
It gives a tight assembly fit where the hole and shaft may need to be
pressed together.
6. Light press fit: H7–p6. This is used where a hole and shaft need
permanent, accurate assembly. The parts need pressing together but the fit
is not so tight that it will overstress the hole bore.
Basic Mechanical Design 285
7. Press fit: H7–s6. This is the tightest practical fit for machine elements
such as bearing bushes. Larger interference fits are possible but are only
suitable for large, heavy, engineering components.
Fig. 11.8 Limits and fits – common combinations
Engineers’ Guide to Rotating Equipment286
Choice of surface finish: ‘rules of thumb’
• Rough turned, with visible tool marks: N10 (12.5 µm Ra)
• Smooth machined surface: N8 (3.2 µm Ra)
• Static mating surfaces (or datums): N7 (1.6 µm Ra)
• Bearing surfaces: N6 (0.8 µm Ra)
• Fine ‘lapped’ surfaces: N1 (0.025 µm Ra)
Finer finishes can be produced but are more suited for precision applications
such as instruments. It is good practice to specify the surface finish of close-
fitting surfaces of machine elements, as well as other BS 308 parameters
such as squareness and parallelism.
11.8 Surface finishSurface finish, more correctly termed ‘surface texture’, is important for all
machine elements that are produced by machining processes such as
turning, grinding, shaping, or honing. This applies to surfaces that are flat or
cylindrical. Surface texture is covered by its own technical standard, BS
1134 Assessment of surface texture. It is measured using the parameter Ra,
which is a measurement of the average distance between the median line of
the surface profile and its peaks and troughs, measured in micrometres
(µm). There is another system from a comparable standard, DIN ISO 1302,
which uses a system of ‘N’ numbers – it is simply a different way of
describing the same thing (see Fig. 11.9).
Fig. 11.9 Surface finish
Basic Mechanical Design 287
11.9 Reliability in design The concept of reliability is an important consideration of rotating
equipment design. There is a well-developed theoretical side to it: quantities
such as MTTF (mean time to failure) and MTBF (mean time between
failures) are in common use in safety-critical applications such as petroleum
and chemical plant design. In essence:
• RELIABILITY IS ABOUT HOW, WHY, AND WHEN THINGS FAIL.
The ‘bathtub curve’
This is so-called for no better reason than it looks, in outline, like a bathtub
(see Fig. 11.10). It indicates when you can expect things to fail and is well
proven, reflecting reasonably accurately what happens to many engineering
products. It tends to be most accurate for complex products, including most
rotating equipment. The chances of failure are quite high in the early
operational life of a product item. This is due to inherent defects or
fundamental design errors in the product, or incorrect assembly of the
multiple component parts. A progressive wear regime then takes over for the
middle 75 per cent of the product’s life – the probability of failure here is
low. As the lifetime progresses, the rate of deterioration increases, causing
progressively higher chances of failure.
Failure mode analysis
Failure mode analysis (FMA) is concerned with how and why failures occur.
In contrast to the bathtub curve there is a strong product-specific bias to this
technique, so generalized ‘results’ rarely have much validity. In theory, most
engineered products will have a large number of possible ways that they can
fail (termed ‘failure modes’). Practically, this reduces to three or four
common types of failure, because of particular design parameters,
distribution of stress, or similar. The technique of FMA is a structured look
at all the possibilities, so that frequently-occurring failure modes can be
anticipated in advance of their occurring, and can be ‘designed out’. FMA is
therefore, by definition, multidisciplinary. Figure 11.11 outlines the
principles of FMA, using as an example a simple compression spring – a
common sub-component of many rotating equipment products.
Risk analysis
This encapsulates a number of assessment techniques that are all
‘probabilistic’. They look at a failure in terms of the probability that it may,
or may not, happen. The techniques tend to be robust in the mathematical
sense, but sometimes have rather limited practical application because the
Engineers’ Guide to Rotating Equipment288
rules of probability are not axiomatic in the engineering world. This means
that risk analysis techniques are fine, as long as you realize the limitations
of their use when dealing with practical engineering designs.
Reliability assessment
The most useful form of reliability assessment involves looking forward,
to try and eliminate problems before they occur, to effect reliability
improvements. There are limitations to this technique:
• it involves anticipation, which is difficult;
• reliability assessment is strictly relative. It may be possible to conclude
that component X should last longer than component Y, but not that
component X will definitely last for 50 000 h;
• it must be combined with sound engineering and design knowledge if it is
to be effective.
Fig. 11.10 Reliability – the ‘bathtub curve’
Basic Mechanical Design 289
11.10 Improving design reliability:
eight principles
Reduce static loadings
It is good practice to reduce static loadings on component parts, by
redistributing loads or increasing loaded areas. The effects are small when
existing design stresses are less than about 30 per cent of yield strength (Re),
but can be significant if they are higher. The amount of deformation of a
component is reduced, which can lead to a decreased incidence of failure.
Low stresses improve reliability.
Reduce dynamic loadings
In many components, stresses caused by dynamic loadings can be several
orders of magnitude higher than ‘static’ design stresses – up to nine or ten
times if shock loads are involved. Dynamic shock loads are, therefore, a
major cause of failure. It is good design practice to eliminate as many shock
loads as possible. This can be done by using design features such as
damping, movement restricters, flexible materials, and by isolating critical
Fig. 11.11 The principles of failure mode analysis (FMA)
Engineers’ Guide to Rotating Equipment290
components from specific externally induced shock loadings. The
possibility of general dynamic stresses can normally be limited by reducing
the relative speed of movement of components. In rotating shafts,
particularly, this has the effect of reducing internal torsional stresses during
starting and braking of the shaft.
Reduce cyclic effects
Cyclic fatigue is the biggest cause of failure of engineering components.
High-speed, low-speed, and normally static components frequently fail in
this way. The mechanism is well known; cyclic stresses as low as 40 per cent
of Re will cause progressive weakening of most materials. One of the major
principles of improving reliability therefore is to reduce cyclic effects
wherever possible. This applies to the amplitude of the loading and to its
frequency. Typical cyclic effects are:
• vibration: this is defined in three orthogonal planes x, y, and z; it is often
caused by residual unbalance of rotating parts;
• pulsations: often caused by pressure fluctuations;
• twisting: in many designs, torsion is cyclic, rather than static; heavy duty
pump shafts and engine crankshafts are good examples;
• deflections: designs that have members which are intended to deflect in
use invariably suffer from cyclic fatigue to some degree. In applications
such as aircraft structures, fatigue life is the prime criterion that
determines the useful life of the product.
Reduce operating temperatures
This applies to the majority of moving components that operate at above-
ambient temperature. Excessively high temperatures, for instance in
bearings and similar ‘contact’ components, can easily cause failure. The
principle of reliability improvement is to increase the design margin
between the operating temperature of a bearing face or lubricant film and its
maximum allowable temperature. Typical actions include increasing cooling
capacity and lubricant flow, or reducing specific loadings. The effect of
temperature on static components is also an important consideration.
Thermal expansion of components with complex geometry can be difficult
to calculate accurately and can lead to unforeseen deflections, movements,
and ‘locked in’ assembly stresses. Stresses induced by thermal expansion of
constrained components can be extremely high, capable of fracturing most
engineering materials quite easily. For low-temperature components
(normally static, such as aircraft external parts or cryogenic pressure
vessels) the problem is the opposite; low temperatures increase the
Basic Mechanical Design 291
brittleness (decrease the Charpy impact resistance) of most materials. This
is hard to ‘design out’ as low temperatures are more often the result of a
component’s environment, rather than its actual design. As a general
principle, aim for component design temperatures as near to ambient as
possible – it helps improve reliability.
Remove stress-raisers
Stress-raisers are sharp corners, grooves, notches, or acute changes of
section that cause stress concentrations under normal loadings. They can be
found on both rotating and static components. The stress concentration
factors of sharp corners and grooves are high, and difficult to determine
accurately. Components that have failed predominantly by a fatigue
mechanism are nearly always found to exhibit a ‘crack initiation point’ – a
sharp feature at which the crack has started and then progressed by a cyclic
fatigue mechanism to failure. There are techniques that can be employed to
reduce stress-raisers:
• use blended radii instead of sharp corners, particularly in brittle
components such as castings;
• for rotating components like drive shafts, keep rotating diameters as
constant as possible. If it is essential to vary the shaft diameter, use a
taper. Avoid sharp shoulders, grooves, keyways, and slots;
• avoid rough surface finishes on rotating components. A rough finish can
act as a significant stress-raiser – the surface of a component is often
furthest from its neutral axis and therefore subject to the highest level of
stress.
Reduce friction
Although friction is an essential part of many engineering designs, notably
machines, it inevitably causes wear. It is good practice, therefore, to aim to
reduce non-essential friction, using good lubrication practice and/or low-
friction materials whenever possible. Lubrication practice is perhaps the
most important one; aspects such as lubricating fluid circuit design,
filtering, flowrates, and flow characteristics can all have an effect on
reliability. If you can keep friction under controlled conditions, you will
improve reliability.
Design for accurate assembly
Large numbers of engineering components and machines fail because they
are not assembled properly. Precision rotating machines such as engines,
gearboxes, and turbines have closely specified running clearances and
Engineers’ Guide to Rotating Equipment292
cannot tolerate much misalignment in assembly. This applies even more to
smaller components such as bearings, couplings, and seals. Reliability can
be improved, therefore, by designing a component so that it can only be
assembled accurately. This means using design features such as keys,
locating lugs, splines, guides, and locating pins which help parts assemble
together accurately. It is also useful to incorporate additional measures to
make it impossible to assemble components the wrong way round or back-
to-front. Accurate assembly can definitely improve reliability (although you
will not find a mathematical theory explaining why).
Isolate corrosive and erosive effects
As a general principle, corrosive and erosive conditions, whether from a
process fluid or the environment, are detrimental to most materials in some
way. They cause failures. It is best to keep them isolated from close-fitting
moving parts – the use of clean flushing water for slurry pump bearings and
shaft seals is a good example. Corrosion and erosion also attack large,
unprotected static surfaces, so highly resistant alloys or rubber/epoxy linings
are often required. Galvanic corrosion is an important issue for small closely
matched component parts of machines – look carefully at the
electrochemical series for the materials being used to see which one will
corrode sacrificially. Good design reliability is about making sure the less
critical components corrode first. It is sometimes possible to change the
properties of the electrolyte (often process or flushing fluid, or oil) to reduce
its conductivity, if a potential difference exists between close-fitting
components and galvanic corrosion problems are expected.
11.11 Design for reliability – a new approachDesign for reliability (DFR) is an evolving method of stating and evaluating
design issues in a way that helps achieve maximum reliability in a design.
The features of this ‘new approach’ are:
• it is a quantitative but visual method – so not too difficult to understand;
• no separate distinction is made between the functional performance of a
design and its reliability – both are considered equally important;
• it does not rely on pre-existing failure rate data (which can be inaccurate).
The technique
Design parameters are chosen with the objective of maximizing all of the
safety margins that will be built in to a product or system. All the possible
modes of failure are investigated and then expressed as a set of design
constraints (see Fig. 11.12). The idea is that a design which has the highest
Basic Mechanical Design 293
safety margin with respect to all the constraints will be the most reliable
(point X in the figure). Constraints are inevitably defined in a variety of
units, so a grading technique is required that yields a non-dimensional
performance measure of each individual constraint.
Fig. 11.12 Design for reliability – expressing
design constraints
Engineers’ Guide to Rotating Equipment294
11.12 Useful references and standards
1. BS 308 Engineering drawing practice (various parts).
2. BS EN 22768-1: (1993) Working limits on toleranced dimensions.
3. BS 4500/BS EN 20286: (1993) ISO system of limits and fits (various
parts).
4. DIN ISO 1302: (1992) Technical drawings – methods of indicating
surface texture.
5. DIN ISO 1101: (1983) Technical drawings.
6. DIN ISO 8015: (1985) Technical drawings – fundamental tolerancing
principles.
7. DIN 4768: (1983) Surface roughness.
8. BS 1134: Assessment of surface texture (various parts).
9. ANSI/ASME Y14.5M: (1994) Dimensioning and tolerancing.
10. ISO 286-1: (1988) ISO system of limits and fits.
CHAPTER 12
Materials of Construction
Material properties are of great importance in all aspects of rotating
equipment design and manufacture. It is essential to check the up-to-date
version of the relevant British Standards or equivalent when choosing or
assessing a material. The most common materials used for rotating
equipment are divided into the generic categories of carbon, alloy, stainless
steel, and non-ferrous.
12.1 Plain carbon steels – basic dataTypical properties are shown in Table 12.1.
Table 12.1 Plain carbon steel: properties
Type %C %Mn Yield, Re UTS, Rm
(MN/m2) (MN/m2)
Low C steel 0.1 0.35 220 320
General structural steel 0.2 1.4 350 515
Steel castings 0.3 – 270 490
12.2 Alloy steels – basic dataAlloy steels have various amounts of Ni, Cr, Mn, or Mo added to improve
properties. Typical properties are shown in Table 12.2.
Engineers’ Guide to Rotating Equipment296
Table 12.2 Alloy steels: properties
Type %C Others (%) Re (MN/m2) Rm (MN/m2)
Ni/Mn steel 0.4 0.85 Mn 480 680
1.00 Ni
Ni/Cr steel 0.3 0.5 Mn 800 910
2.8 Ni
1.0 Cr
Ni/Cr/Mo steel 0.4 0.5 Mn 950 1050
1.5 Ni
1.1 Cr
0.3 Mo
12.3 Stainless steels – basic dataStainless steel is a generic term used to describe a family of steel alloys
containing more than about 11 per cent chromium. The family consists of
four main classes, subdivided into about 100 grades and variants. The main
classes are austenitic and duplex. The other two classes, ferritic and
martensitic, tend to have more specialized application and so are not so
commonly found in general rotating equipment use. The basic
characteristics of each class are given below.
• Austenitic The most commonly used basic grades of stainless steel are
usually austenitic. They have 17–25 per cent Cr, combined with 8–20 per
cent Ni, Mn, and other trace alloying elements which encourage the
formation of austenite. They have low carbon content, which makes them
weldable. They have the highest general corrosion resistance of the family
of stainless steels.
• Ferritic Ferritic stainless steels have high chromium content (>17 per cent
Cr) coupled with medium carbon, which gives them good corrosion
resistance properties rather than high strength. They normally have some
Mo and Si, which encourage the ferrite to form. They are generally non-
hardenable.
• Martensitic This is a high-carbon (up to 2 per cent C), low-chromium (12
per cent Cr) variant. The high carbon content can make it difficult to weld.
• Duplex Duplex stainless steels have a structure containing both austenitic
and ferritic phases. They can have a tensile strength of up to twice that of
straight austenitic stainless steels and are alloyed with various trace
elements to aid corrosion resistance. In general, they are as weldable as
austenitic grades but have a maximum temperature limit, because of the
characteristic of their microstructure.
Table 12.3 gives basic stainless steel data.
Mate
rials
of C
onstru
ctio
n297
AISI Other
classifications
Type + Yield
Fty
(ksi)
[(Re)
MPa]
Ultimate
Ftu
(ksi)
[(Rm)
MPa]
E(%)
50
mm
HRB %C %Cr %
others *
Properties
302 ASTM A296
(cast),
Wk 1.4300,
18/8, SIS 2331
Austenitic 40 [275.8] 90 [620.6] 55 85 0.15 17–19 8–10 Ni A general
purpose
stainless steel.
304 ASTM A296,
Wk 1.4301,
18/8/LC,
SIS 2333,
304S18
Austenitic 42 [289.6] 84 [579.2] 55 80 0.08 18–20 8–12 Ni An economy
grade.
304L ASTM A351,
Wk 1.4306,
18/8/ELC,
SIS 2352,
304S14
Austenitic 39 [268.9] 80 [551.6] 55 79 0.03 18–20 8–12 Ni Low C to avoid
intercrystalline
corrosion after
welding.
316 ASTM A296,
Wk 1.4436,
18/8/Mo,
SIS 2243,
316S18
Austenitic 42 [289.6] 84 [579.2] 50 79 0.08 16–18 10–14
Ni
Addition of Mo
increases
corrosion
resistance.
316L ASTM A351,
Wk 1.4435,
18/8/Mo/ELC,
316S14,
SIS 2353
Austenitic 42 [289.6] 81 [558.5] 50 79 0.03 16–18 10–14
Ni
Low C weldable
variant of 316.
Table 12.3 Stainless steels – basic data
Stainless steels are commonly referred to by their AISI equivalent classification (where appropriate).
Engin
eers
’G
uid
e to
Rota
ting E
quip
ment
298321 ASTM A240,
Wk 1.4541,
18/8/Ti,
SIS 2337,
321S18
Austenitic 35 [241.3] 90 [620.6] 45 80 0.08 17–19 9–12
Ni
Variation of 304
with Ti added to
improve
temperature
resistance.
405 ASTM
A240/A276/
A351,
UNS 40500
Ferritic 40 [275.8] 70 [482.7] 30 81 0.08 11.5–14.5 1 Mn A general purpose
ferritic stainless
steel.
430 ASTM
A176/A240/
A276,
UNS 43000,
Wk 1.4016
Ferritic 50 [344.7] 75 [517.1] 30 83 0.12 14–18 1 Mn Non-hardening
grade with good
acid-resistance.
403 UNS S40300,
ASTM
A176/A276
Martensitic 40 [275.8] 75 [517.1] 35 82 0.15 11.5–13 0.5 Si Turbine grade of
stainless steel.
410 UNS S40300,
ASTM
A176/A240,
Wk 1.4006
Martensitic 40 [275.8] 75 [517.1] 35 82 0.15 11.5–13.5 4.5–6.5
Ni
Used for machine
parts, pump shafts,
etc.
– 255 (Ferralium) Duplex 94 [648.1] 115 [793] 25 280
HV
0.04 24–27 4.5–6.5
Ni
Better resistance to
SCC than 316.
High strength. Max.
temp 575 °F
(301 °C) due to
embrittlement.
– Avesta SAF
2507 §,
UNS S32750
'Super'
duplex
40% ferrite
99 [682.6] 116 [799.8] ~ 25 300
HV
0.02 25 7 Ni,
4 Mo,
0.3 N
* Main constituents only shown.+
All austenitic grades are non-magnetic; ferritic and martensitic grades are magnetic.§
Avesta trade mark.
Table 12.3 Cont.
Materials of Construction 299
12.4 Non-ferrous alloys – basic dataThe term ‘non-ferrous alloys’ is used for those alloy materials that do not
have iron as their base element. The main ones used for mechanical
engineering applications, with their ultimate tensile strength ranges, are:
• nickel alloys 400–1200 MN/m2
• zinc alloys 200–360 MN/m2
• copper alloys 200–1100 MN/m2
• aluminium alloys 100–500 MN/m2
• magnesium alloys 150–340 MN/m2
• titanium alloys 400–1500 MN/m2
The main ones in use are nickel alloys, in which nickel is frequently alloyed
with copper or chromium and iron to produce material with high
temperature and corrosion resistance. Typical types and properties are
shown in Table 12.4.
Table 12.4 Nickel alloys: properties
Alloy type Designation Constituents (%) UTS (MN/m2)
Ni–Cu UNS N04400 66 Ni, 31 Cu, 1 Fe, 415
(‘Monel’) 1 Mn
Ni–Fe ‘Ni lo 36’ 36 Ni, 64 Fe 490
Ni–Cr ‘Inconel 600’ 76 Ni, 15 Cr, 8 Fe 600
Ni–Cr ‘Inconel 625’ 61 Ni, 21 Cr, 2 Fe, 800
9 Mo, 3 Nb
Ni–Cr ‘Hastelloy C276’ 57 Ni, 15 Cr, 6 Fe, 750
1 Co, 16 Mo, 4 W
Ni–Cr ‘Nimonic 80A’ 76 Ni, 20 Cr 800–1200
(age hardenable)
Ni–Cr ‘Inco Waspalloy’ 58 Ni, 19 Cr, 13 Co, 800–1000
(age hardenable) 4 Mo, 3 Ti, 1 Al
12.5 Material traceabilityThe issue of material traceability is an important aspect of the manufacture
of high-integrity rotating equipment. Most technical codes and standards
make provision for quality assurance activities designed to ensure that
materials of construction used in the pressure envelope are traceable.
Figure 12.1 shows the ‘chain of traceability’ which operates for rotating
equipment materials. Note that although all the activities shown are
Engineers’ Guide to Rotating Equipment300
Fig. 12.1 The ‘chain of traceability’ for materials
Materials of Construction 301
available for use (i.e. to be specified and then implemented) this does not
represent a unique system of traceability suitable for all materials. In
practice there are several ‘levels’ in use, depending on both the type of
material and the nature of its final application. The most common document
referenced in the material sections of rotating equipment specifications is
the European Standard EN 10 204: (1991) Metallic products – types of
inspection documents. It provides for two main ‘levels’ of certification:
Class ‘3’ and Class ‘2’ (see Table 12.5).
Table 12.5 Material traceability: EN 10 204 classes
EN 10 204 Document Compliance with: Test Test basis
certificate validation results
type by the order ‘technical included Specific Non-specific
rules’ *
3.1A I • • Yes • –
3.1B M(Q) • • Yes • –
3.1C P • Yes •
3.2 P + M(Q) • Yes • –
2.3 M Yes • –
2.2 M Yes – •
2.1 M • – No – •
I – An independent (third party) inspection organization.
P – The purchaser.
M(Q) – An ‘independent’ (normally QA) part of the material manufacturer's organization.
M – An involved part of the material manufacturer’s organization.
* – Normally the ‘technical rules’ on material properties given in the relevant material standard (and
any applicable technical code).
CHAPTER 13
The Machinery Directives
13.1 The Machinery Directive 98/37/EC –
what is it?The Machinery Directive 98/37/EC is a prominent European ‘new
approach’ directive with major implications for manufacturers and
importers of all types of machinery and components, including most rotating
equipment. The current directive 98/37/EC has evolved from various
previous directives (including 89/392/EEC, 98/368/EEC, and 93/44/EEC)
and, as such, represents a consolidation of the content of these earlier
directives. The Machinery Directive takes its place as one of the family of
New Approach directives that impose identical requirements in every
member state within the European Economic Area (EEA).
In line with all European directives, The Machinery Directive has to be
implemented in each member state by national regulations. In the UK, this
is Statutory Instrument SI 1992/3073 as amended by SI 1994/2063: The
supply of machinery (safety) regulations 1994 (amended). These are
enforced by the Health and Safety Executive (HSE) for machinery used in
the workplace.
13.2 New Approach directivesThe concept of New Approach directives was introduced in 1985 as a move
towards a coherent family of directives that follow a particular construction
– the overall objective being eventual harmonization of technical ‘rules’
across European member states. Because of the difficulty in rationalizing
the technical content of different published technical codes and standards,
new approach directives do not mention specific technical standards but,
instead, contain a set of ‘essential safety requirements’ (ESRs) with which
Engineers’ Guide to Rotating Equipment304
all products covered by the directive must comply. In addition, the
objectives of the ESRs are supported by the content of European
Harmonized Standards.
So, the two alternative ways of complying with a new approach directive
(such as The Machinery Directive 98/37/EC) are:
• compliance with a relevant European Harmonized Standard; this provides
a presumption of conformity with the ESRs in the directive;
• compliance with other, non-harmonized national standards (or no
published standards at all) plus confirmation that the ESRs have been met
in some other way.
There is a further all-encompassing requirement that products must be
accompanied by all the appropriate documentation and must, in fact, be safe.
13.3 The scope of The Machinery DirectiveThe Directive applies to all machinery and ‘safety components’. A definition
is that a machine is defined as ‘an assembly of linked parts or components,
at least one of which moves’.
There are some exclusions from The Directive:
• machines that are already covered by other directives (see Table 13.1);
• equipment that falls within the scope of the Low Voltage Directive
73/23/EEC and 93/68/EEC.
Table 13.1 Exclusions from The Machinery Directive
The following categories of machines are excluded from the jurisdiction of The
Machinery Directive. This is because they are low risk, or because they are of
high risk and, therefore, covered by other directives or requirements (see The
Machinery Directive). They are:
1 Machinery whose only power source is directly applied manual effort,
unless it is a machine used for lifting or lowering loads.
2 Machinery for medical use, used in direct contact with patients.
3 Special equipment for use in fairgrounds and/or amusement parks.
4 Steam boilers, tanks, and pressure vessels.
5 Machinery specially designed or put into service for nuclear purposes
which, in the event of failure, may result in an emission of radioactivity.
6 Radioactive sources forming part of a machine.
7 Firearms.
The Machinery Directives 305
8 Storage tanks and pipelines for petrol, diesel fuel, inflammable liquids,
and dangerous substances.
9 Means of transport, i.e. vehicles and their trailers intended solely for
transporting passengers by air or on road, rail, or water networks, as well
as means of transport insofar as such means are designed for
transporting goods by air, on public road or rail networks, or on water.
(Vehicles used in the mineral extraction industry are not excluded.)
10 Sea-going vessels and mobile offshore units together with equipment on
board such vessels or units.
11 Cableways, including funicular railways, for public or private transport of
persons.
12 Agricultural and forestry tractors.
13 Machines specially designed and constructed for military or police
purposes.
14 Lifts that permanently serve specific levels of buildings and constructions,
having a car moving between guides which are rigid and inclined at an
angle of more than 15 degrees to the horizontal and designed for the
transport of:
– persons;
– persons and goods;
– goods alone if the car is accessible (a person may enter it without
difficulty) and fitted with controls situated inside the car or within reach
of a person inside.
15 Means of transport of persons using rack and pinion rail mounted
vehicles.
16 Mine winding gear.
17 Theatre elevators.
18 Construction site hoists intended for lifting persons or persons and goods.
Old machinery manufactured before 1995 does not have to comply, unless
it is refurbished or upgraded to the extent that its specification is
substantially changed. Some specialized machines are identified by The
Machinery Directive as requiring special test procedures. These are shown
in Table 13.2.
Table 13.1 Cont.
Engineers’ Guide to Rotating Equipment306
Table 13.2 Types of machinery and safety components subject
to ‘special attestation procedures’
A. MACHINERY
1 Circular saws (single or multi-blade) for working with wood and analogous
materials and working with meat and analogous materials:
– sawing machines with fixed tool during operation, having fixed bed with
manual feed of the workpiece or with a demountable power feed;
– sawing machines with fixed tool during operation, having a manually
operated reciprocating saw-bench or carriage;
– sawing machines with fixed tool during operation, having a built-in
mechanical feed device for the workpieces, with manual loading and/or
unloading;
– sawing machines with moveable tool during operation, with a
mechanical feed device and manual loading and/or unloading.
2 Hand-fed surface planing machines for woodworking.
3 Thicknessers for one-side dressing with manual loading and/or unloading
for woodworking.
4 Band-saws with fixed or mobile bed and band saws with a mobile
carriage, with manual loading and/or unloading, for working with wood
and analogous materials and for working with meat and analogous
materials.
5 Combined machines of the types referred to in 1–4 and 7 for working with
wood and analogous materials.
6 Hand-fed tenoning machines with several tool holders for woodworking.
7 Hand-fed vertical spindle moulding machines for working with wood and
analogous materials.
8 Portable chain saws for woodworking.
9 Presses, including press-brakes, for the cold working of metals, with
manual loading and/or unloading, whose movable working parts may
have a travel exceeding 6 mm and a speed exceeding 30 mm/s.
10 Injection or compression plastics-moulding machines with manual loading
or unloading.
11 Injection or compression rubber-moulding machines with manual loading
or unloading.
12 Machinery for underground working of the following types:
– machinery on rails: locomotives and brake-vans;
– hydraulic powered roof supports;
– internal combustion engines to be fitted to machinery for underground
working.
The Machinery Directives 307
13 Manually loaded trucks for the collection of household refuse
incorporating a compression mechanism.
14 Guards and detachable transmission shafts with universal joints as
described in Section 3.4.7 of Annex B.
15 Vehicles servicing lifts.
16 Devices for the lifting of persons involving a risk of falling from a vertical
height of more than three metres.
17 Machines for the manufacture of pyrotechnics.
B. SAFETY COMPONENTS
1 Electro-sensitive devices designed specifically to detect persons in order
to ensure their safety (non-material barriers, sensor mats, electro-
magnetic detectors, etc.).
2 Logic units that ensure the safety functions of bi-manual controls.
3 Automatic moveable screens to protect the presses referred to in 9, 10,
and 11.
4 Roll-over protection structures (ROPS).
5 Falling-object protective structures (FOPS).
Goals, principles, and structures
The overall goals and principles of The Machinery Directive are complex,
but the main points are:
• The manufacturer (or his ‘authorized representative’ in any member state)
is responsible for the machine being safe.
• Design must be based on ‘state of the art’ and ‘good practice’ and
decisions taken during the design and development phases need to be
properly documented to demonstrate this.
• The effect of The Directive, as implemented by statutory instrument in
member states, has most effect on the way that a machinery manufacturer
deals with engineering design development, manufacturing, and
documentation practice rather than the precise form of the end product
(the machine itself).
• Instead of specifying prescriptive technical requirements, The Directive
requires that machines meet a set of essential safety requirements (ESRs).
Most of the ESRs have some direct relation to minimizing safety hazards
that may be present.
Table 13.2 Cont.
Engineers’ Guide to Rotating Equipment308
The structure of The Machinery Directive consists of a series of formal
‘articles’ followed by six main ‘annexes’. These annexes are the most
important content from a design and engineering viewpoint. Table 13.3
summarizes their content.
Table 13.3 The Machinery Directive annexes
Annex I This contains the essential safety requirements (ESRs). A general
part applies to all machinery and specific parts apply specifically
to certain categories of machine.
Annex II This specifies the need for the issue of a certificate or declaration
of conformity that must be provided with every machine supplied
for ‘independent use’ (i.e. for sale).
Annex III Specifies the requirement and method of CE marking to signify
compliance with the directive.
Annex IV This is a list of machinery and safety components that are subject
to special testing procedures that have to be carried out in
conjunction with a Notified Body.
Annex V This describes the EC declaration of conformity and shows the
content of the ‘technical file’.
Annex VI This relates to the criteria for selection, by national authorities, of
Notified Bodies.
13.4 The CE mark – what is it?The CE mark (see Fig. 13.1) probably stands for Communiteé Européen.
Unfortunately, it is far from certain that whoever invented the mark
(probably a bureaucrat in Brussels) had anything particular in mind, other
than to create a logo that would be universally recognized in the European
Union. It is best thought of as simply a convenient logo, without any deeper
meaning. In its current context, a machine can only have the CE mark fixed
to it if it complies with all European directives pertaining to that type of
product, including, if applicable, The Machinery Directive.
Although much ado is made about the application of CE marking to a
machine, the mechanics of the process are in reality fairly straightforward,
each phase being broken down into eight steps (as outlined in Table 13.4).
The Machinery Directives 309
Table 13.4 The steps to CE marking
Step 1 Decide if the product is ‘a machine’, as defined in The Machinery
Directive document itself.
Step 2 Check whether the machine appears on the list of those that are
excluded from the requirements of The Machinery Directive (see
Table 13.1), or whether it falls under the jurisdiction of any other
European directive (such as, for example, the Low Voltage or
Medical Devices Directive), in which case The Machinery
Directive would not apply.
Step 3 Perform a risk assessment to make sure that all potential safety
risks have been eliminated or minimized during the design and
construction of the machine.
Step 4 Demonstrate and record that the Essential Safety Requirements
(ESRs) in Annex I of The Machinery Directive (see Table 13.3)
have been complied with.
OR
Demonstrate and record that the machine has been designed and
manufactured to a European Harmonized Standard, in which
case it will carry a presumption of conformity with The Machinery
Directive (including the ESRs).
Step 5 Check if the machine is specifically listed in Annex IV of The
Machinery Directive. If it is, then it needs special test procedures
applied to it and independent certification by a Notified Body.
Step 6 Assemble a technical file for the machine. This must comply with the
required contents as set out in Annex V of The Machinery Directive.
Step 7 Draw up and sign a declaration of conformity in accordance with
Annex II of The Machinery Directive.
Step 8 Affix the CE marking to the machine, on its nameplate. This needs
to be done in accordance with Annex III of The Machinery
Directive which specifies the minimum height of letters (>5 mm)
and the precise way in which the mark must be displayed.
Fig. 13.1 The CE mark
Engineers’ Guide to Rotating Equipment310
13.5 The technical fileThis is a file of information compiled by the manufacturer. The principle of
The Machinery Directive is that the contents of the technical file must meet
five specific requirements (see Table 13.5) and, by implication, provide
adequate coverage of information relevant to health and safety aspects of the
machinery. Table 13.6 shows the typical content of a technical file.
Table 13.5 Five requirements of the technical file
1. The data in the technical file must be relevant.
2. The information must be complete and correct.
3. The information must be available on time. (The Machinery Directive does
not require that the technical file be physically present at all times, but
rather that the information must be made ‘available within a period of time
commensurate with its importance’.)
4. All information on the machinery must be consistent. Information in
instructions, advertising materials, and the technical file may not conflict.
5. The information must be retrievable.
Table 13.6 Typical content of a technical file
• Manufacturer’s name and address
• Machine identification and description
• General arrangement and/or assembly drawing
• Detailed engineering drawings
• Detailed technical calculations
• Detailed test results
• Relevant technical specifications
• A list of relevant European Harmonized Standards and/or reports
demonstrating compliance with the essential safety requirements (ESRs)
• Detailed operating instructions for the machine
• Quality assurance procedures
• Information on methods used to eliminate hazards
• Information on methods of risk assessment, i.e. measures/methods used
and their results and conclusions
• Details of agreements with any third parties relevant to the design,
manufacture, and testing of the machine
• Relevant commercial (e.g. advertising) documentation
The Machinery Directives 311
The actual level of detail in the technical file depends on the individual
nature of the machine. It has to be kept for ten years after the last product
has been produced.
13.6 The declaration of conformityAnnex II of The Machinery Directive specifies that machines must be
supplied with a ‘declaration of conformity’. This is basically a certificate
provided by the machine’s manufacturer (or, in some cases, importer),
stating that all the requirements of The Machinery Directive have been met.
Table 13.7 shows the minimum acceptable content of the declaration of
conformity and Table 13.8 gives a typical pro-forma example. There is
special provision where a manufactured component is supplied to be
incorporated into an assembly or large machine manufactured by someone
else. In this case a ‘certificate of incorporation’ replaces the declaration of
conformity; see Annex II of The Machinery Directive for details.
Table 13.7 Content of the EC declaration of conformity
An EC declaration of conformity must:
(a) state the business name and full address of:
i) the responsible person; and
ii) where that person is not the manufacturer, of the manufacturer;
(b) contain a description of the machinery to which the declaration relates
which, without prejudice to the generality of the foregoing, includes, in
particular:
i) its make;
ii) type; and
iii) serial number;
(c) indicate all relevant provisions with which the machinery complies;
(d) state, in the case of relevant machinery in relation to which an EC type
examination certificate has been issued, the name and address of the
approved body that issued the certificate and the number of such certificate;
(e) state, in the case of relevant machinery in respect of which a technical file
has been drawn up, the name and address of the approved body to which
the file has been sent or which has drawn up a certificate of adequacy for
the file, as the case may be;
(f) specify (as appropriate) the transposed harmonized standards used;
(g) specify (as appropriate) the national standards and any technical
specifications used; and
(h) identify the person authorized to sign the declaration on behalf of the
responsible person.
Table 13.8 Declaration of conformity (typical)
Declaration of Conformity
We, (manufacturer)
of (address)
declare that the machinery
Make:
Type:
Model:
Serial Number:
Year of Construction:
has been manufactured using the following transposed Harmonised
European Standards and technical specifications:
and is in conformity with: (directives to which the product conforms)
e.g. The Machinery Directive 89/392/EEC as amended by Directive
91/368/EEC, Directive 93/44/EEC, Directive 93/68/EEC, and Directive
98/37/EC,
the Low Voltage Directive 73/23/EEC as amended by Directive 93/68/EEC,
and the EMC Directive 89/336/EEC as amended by Directive 92/31/EEC
and 93/68/EEC.
Signed in: (place)
on the: (date)
Signature:
Name: (responsible person)
Position:
Engineers’ Guide to Rotating Equipment312
The Machinery Directives 313
Table 13.9 Typical layout of machinery instructions
1. PRODUCT INFORMATION
• Supplier information:
– the product (type, mark);
– the supplier;
– the address.
• Accurately describe the intended use of the product as well as the
environment and circumstances under which it should be used. Draw
attention to safety aspects of the usage of the machinery (for example: ‘only
to be used by authorized users’).
• In a separate chapter headed ‘Safety’, describe the safety measures
applied:
– applicable guidelines;
– explanation of safety symbols, pictograms, warnings, etc. used;
– possible dangers when:
– safety instructions are not followed;
– machinery is not used by trained personnel;
– machinery is modified, adapted or changed;
– dangerous user conditions (for example weather conditions);
– what to do if …;
– state when guarantee ends.
• Technical specifications:
– noise levels;
– vibration levels;
– heat;
– radiation.
• Customer service:
– ordering parts;
– where customers can report complaints, requirements, deficiencies.
2. INSTALLATION
• Transport instructions;
• Assembly instructions:
– requirements for the machinery foundation, use of shock absorbers;
– lifting accessories;
– personnel (for example: required knowledge, education level).
• Connection requirements (legal requirements, standards);
Engineers’ Guide to Rotating Equipment314
• Connection of:
– electrical system;
– pneumatic system;
– hydraulic system.
3. USAGE
• Putting into service (first use):
– preparation (filling oil reservoirs, switching on electrical circuits, etc.);
– user instructions for the operator;
– personal protection equipment (safety glasses, helmet, etc.);
– indicate potential dangers to onlookers.
• The authorized user:
– type of person (required ability, experience, knowledge, etc.)
– what additional training, instructions.
• Machinery operation:
– description of the control panel (and/or software interface);
– tools/accessories;
– running in production:
– taking working sequence into account;
– possible fault and warning signals.
• Stopping:
– taking sequence into account;
– safety steps to be taken
– waste oil;
– pressurized air, hydraulics;
– cleaning;
– emergency stop.
• Trouble-shooting:
– to be carried out by operator;
– to be carried out by service personnel.
4. MAINTENANCE
• Who may maintain the machinery (and what can or cannot be done …):
– operator;
– user’s trained personnel (knowledge levels, training);
– supplier’s trained personnel.
• Tests and checks.
• Dangers during maintenance/testing.
Table 13.9 Cont.
The Machinery Directives 315
• Special provisions:
– switching on/off;
– control during operation.
• Safety measures.
• The use of special tools supplied for safe maintenance, cleaning, etc. of the
machinery.
5. ACCESSORIES
• Tools, equipment, accessories.
• Safety components (lifting bolts/eyes, etc.):
– Machinery Directive requirements.
• Original ‘spare parts’ (including order information).
• Additional tools, etc. available.
• Draw attention to:
– expertise of personnel;
– safety measures.
• Timing (intervals, duration, etc.).
Machinery instructions
Under The Directive, machinery has to be supplied with adequate
instructions for its use. Table 13.9 shows typical content that is generally
required.
13.7 The role of technical standardsTraditionally, most EU countries had (and in most cases still have) their own
well-established product standards for all manner of manufactured products,
including many types of rotating (and other) machinery. Inevitably, these
standards differ in their technical and administrative requirements, and often
in the fundamental way that compliance of products with the standards is
assured.
Harmonized standards
Harmonized standards are European standards produced (in consultation
with member states) by the European standards organizations CEN/
CENELEC. There is a Directive 98/34/EC that explains the formal status of
these harmonized standards. Harmonized standards have to be ‘transposed’
by each EU country, which means that they must be made available as
national standards and that any conflicting standards have to be withdrawn
within a given time period.
Table 13.9 Cont.
Engineers’ Guide to Rotating Equipment316
A key point about harmonized standards is that any product that complies
with the standards is automatically assumed to conform to the Essential
Safety Requirements of the New Approach European directive relevant to
the particular product. This is known as the ‘presumption of conformity’.
Once a national standard is transposed from a harmonized standard, then the
presumption of conformity is carried with it.
Note that the following terms appear in various directives, guidance
notes, etc.: (They are all exactly the same thing.)
• essential safety requirements (ESRs);
• essential requirements;
• essential health and safety requirements (EHSRs).
Compliance with harmonized standards is not compulsory, it is voluntary.
Compliance does, however, infer that a product meets the essential safety
requirements (ESRs) of a relevant directive and the product can then carry
the CE mark. Table 13.10 shows the index of ESRs.
Table 13.10 Index of ESRs
The Machinery Directive contains a detailed list of Essential Safety
Requirements (ESRs) (actually termed the Essential Health and Safety
Requirements) relating to the design and construction of machinery and
safety components. The full text (Annex 1 of The Directive) covers more than
30 pages.
This table shows an index of the ESRs, along with the reference number
under which they are listed in Annex 1.
1 ESSENTIAL HEALTH AND SAFETY REQUIREMENTS
1.1 General remarks
1.1.0 Definitions
1.1.1 Principles of safety integration
1.1.2 Materials and products
1.1.3 Lighting
1.1.4 Design of machinery to facilitate its handling
1.2 Controls
1.2.0 Safety and reliability of control systems
1.2.1 Control devices
1.2.2 Starting
1.2.3 Stopping device
1.2.4 Mode selection
1.2.5 Failure of the power supply
The Machinery Directives 317
1.2.6 Failure of the control circuit
1.2.7 Software
1.3 Protection against mechanical hazards
1.3.0 Stability
1.3.1 Risk of break-up during operation
1.3.2 Risks due to falling or ejected objects
1.3.3 Risks due to surfaces, edges, or angles
1.3.4 Risks related to combined machinery
1.3.5 Risks relating to variations in the rotational speed of tools
1.3.6 Prevention of risks related to moving parts
1.3.7 Choice of protection against risks related to moving parts
1.4 Required characteristics of guards and protection devices
1.4.0 General requirement
1.4.1 Special requirements for guards
1.4.2 Special requirements for protection devices
1.5 Protection against other hazards
1.5.0 Electricity supply
1.5.1 Static electricity
1.5.2 Energy supply other than electricity
1.5.3 Errors of fitting
1.5.4 Extreme temperatures
1.5.5 Fire
1.5.6 Explosion
1.5.7 Noise
1.5.8 Vibration
1.5.9 Radiation
1.5.10 External radiation
1.5.11 Laser equipment
1.5.12 Emissions of dust, gases, etc.
1.5.13 Risk of being trapped in a machine
1.5.14 Risk of slipping, tripping, or falling
1.6 Maintenance
1.6.0 Machinery maintenance
1.6.1 Machine operating position and servicing points
1.6.2 Isolation of energy sources
1.6.3 Operator intervention
Table 13.10 Cont.
1.6.4 Cleaning of internal parts
1.7 Indicators
1.7.0 Information devices
1.7.1 Warning devices
1.7.2 Warning of residual risks
1.7.3 Marking
1.7.4 Instructions
2 ESSENTIAL HEALTH AND SAFETY REQUIREMENTS FOR CERTAIN
CATEGORIES OF MACHINERY
2.1 Agri-foodstuffs machinery
2.2 Portable hand-held and/or hand-guided machinery
2.3 Machinery for working wood and analogous materials
3 ESSENTIAL HEALTH AND SAFETY REQUIREMENTS TO OFFSET
THE PARTICULAR HAZARDS DUE TO THE MOBILITY OF
MACHINERY
3.1 General
3.1.1 Definition
3.1.2 Lighting
3.1.3 Design of machinery to facilitate its handling
3.2 Work stations
3.2.1 Driving position
3.2.2 Seating
3.2.3 Other places
3.3 Controls
3.3.1 Control devices
3.3.2 Starting/moving
3.3.3 Travelling function
3.3.4 Movement of pedestrian-controlled machinery
3.3.5 Control circuit failure
3.4 Protection against mechanical hazards
3.4.1 Uncontrolled movements
3.4.2 Risk of break-up during operation
3.4.3 Rollover
3.4.4 Falling objects
3.4.5 Means of access
3.4.6 Towing devices
3.4.7 Transmission of power between self-propelled machinery
(or tractor) and recipient machinery
Engineers’ Guide to Rotating Equipment318
Table 13.10 Cont.
The Machinery Directives 319
3.4.8 Moving transmission parts
3.5 Protection against other hazards
3.5.1 Batteries
3.5.2 Fire
3.5.3 Emissions of dust, gases, etc.
3.6 Indications
3.6.1 Signs and warnings
3.6.2 Marking
3.6.3 Instruction handbook
4 ESSENTIAL HEALTH AND SAFETY REQUIREMENTS TO OFFSET
THE PARTICULAR HAZARDS DUE TO A LIFTING OPERATION
4.1 General remarks
4.1.1 Definitions
4.1.2 Protection against mechanical hazards
4.1.2.1 Risks due to lack of stability
4.1.2.2 Guide rails and rail tracks
4.1.2.3 Mechanical strength
4.1.2.4 Pulleys, drums, chains, or ropes
4.1.2.5 Separate lifting accessories
4.1.2.6 Control of movements
4.1.2.7 Handling of loads
4.1.2.8 Lighting
4.2 Special requirements for machinery whose power source is
other than manual effort
4.2.1 Controls
4.2.1.1 Driving position
4.2.1.2 Seating
4.2.1.3 Control devices
4.2.1.4 Loading control
4.2.2 Installation guided by cables
4.2.3 Risks to exposed persons. Means of access to driving
position and intervention points
4.2.4 Fitness for purpose
4.3 Marking
4.3.1 Chains and ropes
4.3.2 Lifting accessories
4.3.3 Machinery
Table 13.10 Cont.
Engineers’ Guide to Rotating Equipment320
4.4 Instruction handbook
4.4.1 Lifting accessories
4.4.2 Machinery
5 ESSENTIAL HEALTH AND SAFETY REQUIREMENTS FOR MA-
CHINERY INTENDED FOR UNDERGROUND WORK
5.1 Risks due to lack of stability
5.2 Movement
5.3 Lighting
5.4 Control devices
5.5 Stopping
5.6 Fire
5.7 Emissions of dust, gases, etc.
6 ESSENTIAL HEALTH AND SAFETY REQUIREMENTS TO OFFSET
THE PARTICULAR HAZARDS DUE TO THE LIFTING OR MOVING
OF PERSONS
6.1 General
6.1.1 Definition
6.1.2 Mechanical strength
6.1.3 Loading control for types of device moved by power other
than human strength
6.2 Controls
6.2.1 Where safety requirements do not impose other solutions
6.3 Risks of persons falling from the carrier
6.4 Risks of the carrier falling or overturning
6.5 Markings
National standards
EU countries are at liberty to keep their national product standards if they
wish. Products manufactured to these do not, however, carry the
presumption of conformity with relevant directives, hence the onus is on the
manufacturer to prove compliance with the ESRs to a Notified Body (on a
case-by-case basis). Once compliance has been demonstrated, then the
product can carry the CE mark.
The process of harmonization of standards is ongoing. Inevitably, given
the high number and complexity of national standards that exist, harmonized
standards are being produced more quickly in some technical fields than in
others. Table 13.11 lists the current ones for common types of rotating
equipment and Table 4.4 some covering wider, generic technical ones such
as vibration, noise, etc.
Table 13.10 Cont.
The Machinery Directives 321
Table 13.11 Some harmonized standards relevant to
The Machinery Directive
Organization Reference Title of the harmonized standards
CEN EN 115/A1: 1998 Safety rules for the construction and
installation of escalators and
passenger conveyors.
CEN EN 201/A1: 2000 Rubber and plastics machines –
Injection moulding machines –
Safety requirements.
CEN EN 289: 1993 Rubber and plastics machinery –
Compression and transfer moulding
presses – Safety requirements for
the design.
CEN EN 292-1: 1991 Safety of machinery – Basic
concepts, general principles for
design – Part 1: Basic terminology,
methodology.
CEN EN 292-2/A1: 1995 Safety of machinery – Basic
concepts, general principles for
design – Part 2: Technical principles
and specifications.
CEN EN 294: 1992 Safety of machinery – Safety
distance to prevent danger zones
being reached by the upper limbs.
CEN EN 349: 1993 Safety of machinery – Minimum
gaps to avoid crushing of parts of
the human body.
CEN EN 418: 1992 Safety of machinery – Emergency
stop equipment, functional aspects –
Principles for design.
CEN EN 457: 1992 Safety of machinery – Auditory
danger signals – General
requirements, design, and testing
(ISO 7731: 1986, modified).
CEN EN 474-1/A1: 1998 Earth-moving machinery – Safety –
Part 1: General requirements.
CEN EN 547-1: 1996 Safety of machinery – Human body
measurements – Part 1: Principles
for determining the dimensions
required for openings for the whole
body access into machinery.
Engineers’ Guide to Rotating Equipment322
CEN EN 547-2: 1996 Safety of machinery – Human body
measurements – Part 2: Principles
for determining the dimensions
required for access openings.
CEN EN 547-3: 1996 Safety of machinery – Human body
measurements – Part 3:
Anthropometric data.
CEN EN 563: 1994 Safety of machinery – Temperatures
of touchable surfaces – Ergonomics
data to establish temperature limit
values for hot surfaces.
CEN EN 574: 1996 Safety of machinery – Two-hand
control devices – Functional aspects
– Principles for design.
CEN EN 614-1: 1995 Safety of machinery – Ergonomic
design principles – Part 1:
Terminology and general principles.
CEN EN 626-1: 1994 Safety of machinery – Reduction of
risks to health from hazardous
substances emitted by machinery –
Part 1: Principles and specifications
for machinery manufacturers.
CEN EN 626-2: 1996 Safety of machinery – Reduction of
risk to health from hazardous
substances emitted by machinery –
Part 2: Methodology leading to
verification procedures.
CEN EN 692: 1996 Mechanical presses – Safety.
CEN EN 809: 1998 Pumps and pump units for liquids –
Common safety requirements.
CEN EN 842: 1996 Safety of machinery – Visual danger
signals – General requirements,
design, and testing.
CEN EN 894-1: 1997 Safety of machinery – Ergonomics
requirements for the design of
displays and control actuators – Part
1: General principles for human
interactions with displays and control
actuators.
CEN EN 894-2: 1997 Safety of machinery – Ergonomics
requirements for the design of
displays and control actuators – Part
2: Displays.
Table 13.11 Cont.
The Machinery Directives 323
CEN EN 953: 1997 Safety of machinery – Guards –
General requirements for the design
and construction of fixed and
movable guards.
CEN EN 954-1: 1996 Safety of machinery – Safety-related
parts of control systems – Part 1:
General principles for design.
CEN EN 981: 1996 Safety of machinery – System of
auditory and visual danger and
information signals.
CEN EN 982: 1996 Safety of machinery – Safety
requirements for fluid power
systems and their components –
Hydraulics.
CEN EN 983: 1996 Safety of machinery – Safety
requirements for fluid power
systems and their components –
Pneumatics.
CEN EN 999: 1998 Safety of machinery – The
positioning of protective equipment
in respect of approach speeds of
parts of the human body.
CEN EN 1032/A1: 1998 Mechanical vibration – Testing of
mobile machinery in order to
determine the whole-body vibration
emission value – General –
Amendment 1.
CEN EN 1037: 1995 Safety of machinery – Prevention of
unexpected start-up.
CEN EN 1050: 1996 Safety of machinery – Principles for
risk assessment.
CEN EN 1088: 1995 Safety of machinery – Interlocking
devices associated with guards –
Principles for design and selection.
CEN EN 1299: 1997 Mechanical vibration and shock –
Vibration isolation of machines –
Information for the application of
source isolation.
CEN EN 1760-1: 1997 Safety of machinery – Pressure-
sensitive protective devices – Part 1:
General principles for the design
and testing of pressure-sensitive
mats and pressure-sensitive floors.
Table 13.11 Cont.
Engineers’ Guide to Rotating Equipment324
CEN EN ISO 3743-1: 1995 Acoustics – Determination of sound
power levels of noise sources –
Engineering methods for small,
movable sources in reverberant
fields – Part 1: Comparison method
for hard-walled test rooms (ISO
3743-1: 1994).
CEN EN ISO 3743-2: 1996 Acoustics – Determination of sound
power levels of noise sources using
sound pressure – Engineering
methods for small, movable sources
in reverberant fields – Part 2:
Methods for special reverberation
test rooms (ISO 3743-2: 1994).
CEN EN ISO 3744: 1995 Acoustics – Determination of sound
power levels of noise sources using
sound pressure – Engineering
method in an essentially free field
over a reflecting plane (ISO 3744:
1994).
CEN EN ISO 3746: 1995 Acoustics – Determination of sound
power levels of noise sources using
sound pressure – Survey method
using an enveloping measurement
surface over a reflecting plane (ISO
3746: 1995).
CEN EN ISO 4871: 1996 Acoustics – Declaration and
verification of noise emission values
of machinery and equipment (ISO
4871: 1996).
CEN EN ISO 9614-1: 1995 Acoustics – Determination of sound
power levels of noise sources using
sound intensity – Part 1:
Measurement at discrete points (ISO
9614-1: 1993).
CEN EN ISO 11200: 1995 Acoustics – Noise emitted by
machinery and equipment –
Guidelines for the use of basic
standards for the determination of
emission sound pressure levels at a
work station and at other specified
positions (ISO 11200: 1995).
Table 13.11 Cont.
The Machinery Directives 325
CEN EN ISO 11201: 1995 Acoustics – Noise emitted by
machinery and equipment –
Measurement of emission sound
pressure levels at a work station and
at other specified positions –
Engineering method in an
essentially free field over a reflecting
plane (ISO 11201: 1995).
CEN EN ISO 11202: 1995 Acoustics – Noise emitted by
machinery and equipment –
Measurement of emission sound
pressure levels at a work station and
at other specified positions – Survey
method in situ (ISO 11202: 1995).
CEN EN ISO 11203: 1995 Acoustics – Noise emitted by
machinery and equipment –
Determination of emission sound
pressure levels at a work station and
at other specified positions from the
sound power level (ISO 11203: 1995).
CEN EN ISO 11204: 1995 Acoustics – Noise emitted by
machinery and equipment –
Measurement of emission sound
pressure levels at a work station and
at other specified positions –
Method requiring environmental
corrections (ISO 11204: 1995).
CEN EN ISO 11546-1: 1995 Acoustics – Determination of sound
insulation performances of
enclosures – Part 1: Measurements
under laboratory conditions (for
declaration purposes) (ISO 11546-1:
1995).
CEN EN ISO 11546-2: 1995 Acoustics – Determination of sound
insulation performances of
enclosures – Part 2: Measurements
in situ for acceptance and
verification purposes (ISO 11546-2:
1995).
CEN EN ISO 13753: 1998 Mechanical vibration and shock –
Hand–arm vibration – Method for
measuring the vibration
transmissibility of resilient materials
when loaded by the hand–arm
system (ISO 13753: 1998).
Table 13.11 Cont.
Engineers’ Guide to Rotating Equipment326
CENELEC EN 61310-1: 1995 Safety of machinery – Indication,
marking, and actuation – Part 1:
Requirements for visual, auditory,
and tactile signals (IEC 61310-1:
1995).
CENELEC EN 61310-2: 1995 Safety of machinery – Indication,
marking, and actuation – Part 2:
Requirements for marking (IEC
61310-2: 1995).
CENELEC EN 61310-3: 1999 Safety of machinery – Indication,
marking, and actuation – Part 3:
Requirements for the location and
operation of actuators (IEC 61310-3:
1999).
CENELEC EN 61496-1: 1997 Safety of machinery – Electro-
sensitive protective equipment –
Part 1: General requirements and
tests (IEC 61496-1: 1997).
13.8 The proposed ‘amending’ directive
95/16/ECThere are currently proposals for an amending directive 95/16/EC, which
would effectively ‘re-cast’ the content of the consolidating Machinery
Directive 98/37/EC. The stated purpose is to clarify the content of The
Machinery Directive and leave it less open to incorrect interpretation. The
amendments are based on a set of twelve proposals set out at the beginning
of the 95/16/EC document. Table 13.12 outlines some of the changes (refer
to the document itself for full details).
Table 13.11 Cont.
The Machinery Directives 327
Table 13.12 Some changes to The Machinery Directive
proposed by 95/16/EC
Articles
Article 1 has been very substantially amended to take account of comments
to the effect that not all of the products referred to in The Directive are
machines in the strict sense of the word. The new definition takes account of
this aspect and clearly identifies partly completed machinery, to which The
Directive does not apply in its entirety.
A number of definitions have been added to make it easier to interpret the
text. In the case of safety components, it was decided to present an
exhaustive list of machinery rather than a definition (the text of Directive
98/37/EC contains such a definition and it has given rise to many problems of
interpretation). In order to take account of technological development, the
Machinery Committee set up by The Directive will have the powers to amend
this list.
Annex I – Essential health and safety requirements
The essential health and safety requirements set out in Annex I have not been
fundamentally changed; the numbering of the various points has been
maintained wherever possible. Many of the changes to the original text
concern the drafting.
Annex II – Declarations
The contents of the declarations described in Annex II have been amended to
take account of the incorporation of safety components into machinery. There
are now only two types of declaration: the ‘EC conformity declaration’ for
all machinery and the ‘declaration of incorporation’ for partly completed
machinery.
Annex IV – Categories of potentially hazardous machinery
The list in Annex IV of machinery regarded as most hazardous has been
amended to take account of the difficulties of interpreting the existing list.
Annexes V and VIII on partly completed machinery and intrinsically safe
machinery
A specific annex setting out the assembly instructions for partly completed
machinery has been added (Annex V). The same goes for the conformity
assessment of a machine not exhibiting any intrinsic health and safety
hazard (Annex VIII).
Annexes VI, VII, IX, and XI on conformity assessment
The content of these annexes, which corresponds to the modules set out in
Decision 93/465/EEC (Annexes VI, VII, X, and XI), has been maintained,
although the wording has been changed to make them easier to use.
Engineers’ Guide to Rotating Equipment328
The technical file which is included in a number of modules is now the
subject of a separate annex (Annex VI).
Annex IX on the adequacy of a machine in respect of harmonized
standards has been added to take account of the practice in the 1989
Directive, which was drafted before the modules were adopted. This
procedure is a major simplification for manufacturers who have elected to
manufacture their machinery in accordance with harmonized standards.
In Annex IX (adequacy in respect of harmonized standards) and Annex X
(EC type-examination), it has been specified that the Notified Body must keep
its technical file for 15 years. This detail does not appear in the modules.
Annex XI on fully quality assurance has been amended, relative to the
corresponding module, to make it clear that the manufacturer must, for each
of the machines he manufactures, possess a technical file so as to be able to
respond to any reasoned request from a member state which might consider
that the machinery in question is defective.
13.9 Useful references and standardsNew Approach directives and harmonized standards are listed on:
http://europa.eu.int/comm./enterprise/newapproach/standardization/harmstds/
Information can be obtained from:
Standardization unit – European Commission
Mr D Herbert
European Commission
rue de la Loi 200
B-1049
Brussels
Contact person: Ingrid.gillisjans@cec.eu.ir
European standards organization
• CEN: infodesk@cenorm.be
• CENELEC: general@cenelec.be
• ETSI: infocentre@etsi.fr
Machinery Directive 98/37/EC
The general website, giving access to all the text (including Annexes I–VII), is:
http://europa.eu.int/comm./enterprise/mechan_equipment/machinery/guide/
content.htm
Information on The Directive can be obtained from:
• EC-DG ENTR G.3
• Mr Van Gheluwe, Tel: 00 32 (2) 296 09 64, Fax: 00 32 (2) 296 62 73
• e-mail: machinery@cec.eu.int
Table 13.12 Cont.
CHAPTER 14
Organizations and Associations
The following table shows some major European and American associations
and organizations relevant to rotating equipment activities.
Acronym Organization Contact
ABMA American Bearing
Manufacturers Association
2025 M Street NW
Suite 800
Washington DC 20036
Tel: 00 1 (202) 367 1155
Fax: 00 1 (202) 367 2155
www.abma-dc.org
ABS American Bureau of
shipping (UK)
ABS House
1 Frying Pan Alley
London
E1 7HR
Tel: +44 (0)20 7247 3255
Fax: +44 (0)20 7377 2453
www.eagle.org
ACEC American Consulting
Engineers Council
1015, 15th St NW #802
Washington DC 20005
Tel: 00 1 (202) 347 7474
Fax: 00 1 (202) 898 0068
www.acec.org
AEAT AEA Technology plc (UK)
Harwell
Didcot
Oxon
OX11 0QT
Tel: +44 (0)1235 821111
Fax: +44 (0)1235 432916
www.aeat.co.uk
AGMA American Gear
Manufacturers Association
1500 King St
Suite 201
Alexandria VA 22314
Tel: 00 1 (703) 684 0211
Fax: 00 1 (703) 684 0242
www.agma.org
Engineers’ Guide to Rotating Equipment330
ANS American Nuclear Society
555 N. Kensington Ave
La Grange Park
IL 60526
Tel: 00 1 (708) 352 6611
Fax: 00 1 (708) 352 0499
www.ans.org
ANSI American National
Standards Institute
11, W. 42nd St
New York
NY 10036
Tel: 00 1 (212) 642 4900
Fax: 00 1 (212) 398 0023
www.ansi.org
API American Petroleum
Institute
1220 L St NW
Washington
DC 20005
Tel: 00 1 (202) 682 8000
Fax: 00 1 (202) 682 8232
www.api.org
ASERCOM Association of European
Refrigeration Compressor
Manufacturers
C/O Copeland GmbH
Eichborndamm 141-175
D-1000 Berlin
Germany
Tel: 00 (49) 30 419 6352
Fax: 00 (49) 30 419 6205
www.hvacmall.com
ASHRAE American Society of
Heating, Refrigeration and
Air Conditioning Engineers
1791 Tullie Circle NE
Atlanta
GA 30329
Tel: 00 1 (404) 636 8400
Fax: 00 1 (404) 321 5478
www.ashrae.org
ASME American Society of
Mechanical Engineers
3, Park Ave
New York
NY 10016-5990
Tel: 00 1 (973) 882 1167
Fax: 00 1 (973) 882 1717
www.asme.org
ASNT American Society for Non-
Destructive Testing
1711 Arlington Lane
Columbus
OH 43228-0518
Tel: 00 1 (614) 274 6003
Fax: 00 1 (614) 274 6899
www.asnt.org
ASTM American Society for
Testing of Materials
100, Barr Harbor Drive
W Conshohocken
PA 19428-2959
Tel: 00 1 (610) 832 9585
Fax: 00 1 (610) 832 9555
www.ansi.org
Organizations and Associations 331
AWS American Welding Society
550 NW Le Jeune Rd
Miami
FL 33126
Tel: 00 1 (305) 443 9353
Fax: 00 1 (305) 443 7559
www.awweld.org
AWWA American Water Works
Association Inc
6666 W Quincy Ave
Denver
CO 80235
Tel: 00 1 (303) 794 7711
Fax: 00 1 (303) 794 3951
www.awwa.org
BCAS British Compressed Air
Society
33-34 Devonshire St
London
W1G 6YP
Tel: +44 (0)20 7935 2464
Fax: +44 (0)20 7935 2464
www.britishcompressedair.
co.uk
BCEMA British Combustion
Equipment Manufacturers
Association
The Fernery
Market Place
Midhurst
W Sussex
GU29 9DP
Tel: +44 (0)1730 812782
Fax: +44 (0)1730 813366
www.bcema.co.uk
BFPA British Fluid Power
Association
Cheriton House
Cromwell Business Park
Chipping Norton
Oxon
OX7 5SR
Tel: +44 (0)1608 647900
Fax: +44 (0)1608 647919
www.bfpa.co.uk
BGA British Gear Association
Suite 43 Inmex Business
Park
Shobnall Rd
Burton on Trent
Staffordshire
DE14 2AU
Tel: +44 (0)1283 515521
Fax: +44 (0)1283 515841
www.bga.org.uk
BIE British Inspecting Engineers
Chatsworth Technology
Park
Dunston Road
Chesterfield
D41 8XA
Tel: +44 (0)1246 260260
Fax: +44 (0)1246 260919
www.bie-international.com
Engineers’ Guide to Rotating Equipment332
B.Inst.NDT British Institute of Non
Destructive Testing
1 Spencer Parade
Northampton
NN1 5AA
Tel: +44 (0)1604 259056
Fax: +44 (0)1604 231489
www.bindt.org
BPMA British Pump Manufacturers
Association
The McLaren Building
35 Dale End
Birmingham
B4 7LN
Tel: +44 (0)121 200 1299
Fax: +44 (0)121 200 1306
www.bpma.org.uk
BSI British Standards Institution
Marylands Avenue
Hemel Hempstead
Herts
HP2 4SQ
Tel: +44 (0)1442 230442
Fax: +44 (0)1442 231442
www.bsi.org.uk
BVAMA British Valve and Actuator
Manufacturers Association
The McLaren Building
35 Dale End
Birmingham
B4 7LN
Tel: +44 (0)121 200 1297
Fax: +44 (0)121 200 1308
www.bvama.org.uk
CEN European Committee for
Standardisation (Belgium)
36, rue de Stassart
B-1050
Brussels
Belgium
Tel: 00 (32) 2 550 08 11
Fax: 00 (32) 2 550 08 19
www.cenorm.be
www.newapproach.org
DNV Det Norske Veritas (UK)
Palace House
3 Cathedral Street
London
SE1 9DE
Tel: +44 (0)20 7357 6080
Fax: +44 (0)20 357 76048
www.dnv.com
DTI DTI STRD 5 (UK)
Peter Rutter
STRD5
Department of Trade and
Industry, Room 326
151 Buckingham Palace
Road
London
SW1W 9SS
Tel: +44 (0)20 7215 1437
www.dti.gov.uk/strd
Organizations and Associations 333
DTI DTI Publications Orderline
(UK)
Tel: +44 (0)870 1502 500
Fax: +44 (0)870 1502 333
EC The Engineering Council
(UK)
10 Maltravers Street
London
WC2R 3ER
Tel: +44 (0)20 7240 7891
Fax: +44 (0)20 7240 7517
www.engc.org.uk
EIS Engineering Integrity
Society (UK)
5 Wentworth Avenue
Sheffield
S11 9QX
Tel: +44 (0)114 262 1155
Fax: +44 (0)114 262 1120
www.demon.co.uk/e-i-s
EMA Engine Manufacturers
Association (USA)
2 N LaSalle St
Suite 2200
Chicago
IL 60602
Tel: 00 1 (312) 827 8700
Fax: 00 1 (312) 827 8737
www.engine-manufacturers.
org
FCI Fluid Controls Institute Inc
(USA)
PO Box 1485
Pompano Beach
FL 33061
Tel: 00 1 (216) 241 7333
Fax: 00 1 (216) 241 0105
www.fluidcontrolsinstitute.org
FMG Factory Mutual Global
(USA)
Westwood Executive
Center
100 Lowder Brook Drive
Suite 1100
Westwood
MA 02090-1190
Tel: 00 1 (781) 326 5500
Fax: 00 1 (781) 326 6632
www.fmglobal.com
HI Hydraulic Institute (USA)
9 Sylvian Way
Parsippany
NJ 07054
Tel: 00 1 (973) 267 9700
Fax: 00 1 (973) 267 9055
www.pumps.org
HMSO Her Majesty's Stationery
Office
www.hmso.gov.uk/legis.htm
www.hmso.gov.uk/si
www.legislation.hmso.gov.uk
HSE HSE Books (UK)
PO Box 1999
Sudbury
Suffolk
CO10 6FS
Tel: +44 (0)1787 881165
Fax: +44 (0)1787 313995
www.hse.gov.uk/hsehome
Engineers’ Guide to Rotating Equipment334
HSE HSE's InfoLine (fax
enquiries)
HSE Information Centre
Broad Lane
Sheffield
S3 7HQ
Fax: +44 (0)114 289 2333
www.hse.gov.uk/hsehome
HTRI Heat Transfer Research Inc
(USA)
1500 Research Parkway
Suite 100
College Station
TX 77845
Tel: 00 1 (409) 260 6200
Fax: 00 1 (409) 260 6249
www.htrinet.com
IGTI International Gas Turbine
Institute (ASME)
5775-B Glenridge Dr.
#370
Atlanta
GA 30328
Tel: 00 1 (404) 847 0072
Fax: 00 1 (404) 847 0151
www.asme.org/igti
IMechE The Institution of Mechanical
Engineers (UK)
1 Birdcage Walk
London
SW1H 9JJ
Tel: +44 (0)20 7222 7899
Fax: +44 (0)20 7222 4557
www.imeche.org.uk
IoC The Institute of Corrosion
(UK)
4 Leck Street
Leighton Buzzard
Bedfordshire
LU7 9TQ
Tel: +44 (0)1525 851771
Fax: +44 (0)1525 376690
www.icorr.demon.co.uk
IoE The Institute of Energy (UK)
18 Devonshire Street
London
W1N 2AU
Tel: +44 (0)20 7580 7124
Fax: +44 (0)20 7580 4420
www.instenergy.org.uk
IoM The Institute of Materials
(UK)
1 Carlton House Terrace
London
SW1Y 5DB
Tel: +44 (0)20 7451 7300
Fax: +44 (0)20 7839 1702
www.instmat.co.uk
IPLantE The Institution of Plant
Engineers (UK)
77 Great Peter Street
Westminster
London
SW1P 2EZ
Tel: +44 (0)20 7233 2855
Fax: +44 (0)20 7233 2604
www.iplante.org.uk
Organizations and Associations 335
IQA The Institute of Quality
Assurance (UK)
12 Grosvenor Crescent
London
SW1X 7EE
Tel: +44 (0)20 7245 6722
Fax: +44 (0)20 7245 6755
www.iqa.org
ISO International Standards
Organization (Switzerland)
PO Box 56
CH-1211
Geneva
Switzerland
Tel: 00 (22) 749 011
Fax: 00 (22) 733 3430
www.iso.ch
LR Lloyd's Register (UK)
71 Fenchurch St
London
EC3M 4BS
Tel: +44 (0)20 7709 9166
Fax: +44 (0)20 7488 4796
www.lrqa.com
MSS Manufacturers
Standardization Society of
the Valve and Fittings
Industry (USA)
127 Park Street NE
Vienna
VA 22180-4602
Tel: 00 1 (703) 281 6613
Fax: 00 1 (703) 281 6671
www.mss-hq.com
NACE National Association of
Corrosion Engineers (USA)
1440 South Creek Drive
Houston
TX 77084-4906
Tel: 00 1 (281) 228 6200
Fax: 00 1 (281) 228 6300
www.nace.org
NFP National Fire Protection
Association (USA)
1, Batterymarch Park
PO Box 9101
Quincy
MA 02269-9101
Tel: 00 1 (617) 770 3000
Fax: 00 1 (617) 770 0700
www.nfpa.org
NFPA National Fluid Power
Association (USA)
3333 N Mayfair Rd
Milwaukee
WI 53222-3219
Tel: 00 1 (414) 778 3344
Fax: 00 1 (414) 778 3361
www.nfpa.com
NIST National Institute of
Standards and Technology
(USA)
100 Bureau Drive
Gaithersburg
MD 20899-0001
Tel: 00 1 (301) 975 8205
Fax: 00 1 (301) 926 1630
www.nist.gov
Engineers’ Guide to Rotating Equipment336
PDA Pump Distributors
Association
5 Chapelfield
Orford
Woodbridge
IP12 2HW
Tel: +44 (0)1394 450181
Fax: +44 (0)1394 450181
www.pda-uk.com
SAE Society of Automotive
Engineers
400 Commonwealth Drive
Warrendale
PA 10509-6001
Tel: 00 1 (724) 776 4841
Fax: 00 1 (724) 776 5760
www.sae.org
SAFeD Safety Assessment
Federation (UK)
Nutmeg House
60 Gainsford Street
Butlers Wharf
London
SE1 2NY
Tel: +44 (0)20 7403 0987
Fax: +44 (0)20 7403 0137
www.safed.co.uk
TUV TUV (UK) Ltd
Surrey House
Surrey St
Croydon
CR9 1XZ
Tel: +44 (0)20 8680 7711
Fax: +44 (0)20 8680 4035
www.tuv-uk.com
UKAS The United Kingdom
Accreditation Service
21-47 High Street
Feltham
Middlesex
TW13 4UN
Tel: +44 (0)20 8917 8554
Fax: +44 (0)20 8917 8500
www.ukas.com
VGT Verenigning Gas Turbine
(Dutch Gas Turbine
Association)
Burgemeester
Verderiaan 13
3544 AD Utrecht
PO Box 261
3454 ZM De Meern
Netherlands
Tel: 00 (31) 30 669 1966
Fax: 00 (31) 30 669 1969
www.vgt.org/vgt
95/16/EC 32698/37/EC 30398/37/EC 328
Acceleration 13, 68angular 68linear 68
Activity factor 266Aero turbojet 225Aeropropeller 263
design 264Afterburner 223Algebra, vector 27Alloy steels 295, 296Analysis:
dimensional 21failure mode 287risk 287
API 613 249Area 15Axial flow compressor characteristics
235Axisymmetric flows 151
Balance:calculations 173of couplings 97quality grades (ISO 1940) 75
Balancing:dynamic 78pump impeller 174pump rotor 175rotor dynamic 244standards 79
Ball bearings 88Beams:
deflection of 51, 52slope of 51, 52
Bearing housing vibration 75Bearings 86
GT 240GT shaft 241lifetime 86sensors, GT 242standards 131
Bellows seals 110Belt:
drives 121V 124wedge 124
Bending and torsion, combined 60Blade clearance checks 245Blade element design theory 263Boundary layers 145Brakes 128
basic types 129
Cam:constant velocity 119simple harmonic motion 120uniform acceleration 120
CE mark 308Centrifual pump test circuit 165Centrifugal draught fan 267Centrifugal pumps 153Chain of traceability 299Characteristics:
GT noise 247pump 162
Clearance checks:blade 245GT 246
Clutches 123friction 127
Coefficients of friction 89Combustion arrangement, GT
sequential 238Compressibility 136Compressible one-dimensional flow
147
Index
Engineers’ Guide to Rotating Equipment338
Compressor 181acceptance testing 183flowrate 181geometry 262performance 181specifications and standards 186test circuit 184technical standards 186
Constant velocity cam 119Contact checks 250Couplings:
balance of 97flexible 93, 96fluid 123gear 94keyed 57shaft 91
Crankshaft web deflections 258
Datums 278Declaration of conformity 311, 312Deflection of beams 51, 52Density 5Design:
aeropropellers 264constraints 293for reliability 292, 293reliability, improving 289reliability in 287theory, blade element 263
Diesel engine 255brake test 257guarantee 256performance 255technical standards 259
Differential pulleys 130Dimensional analysis 21Disc-type flexible couplings 93Double helical gears 103Drag coefficients 151Draught fan, centrifugal 267Dynamic balancing 78
of a gear rotor 251test 250
Dynamic equilibrium 65Dynamic viscosity 16
Elastic bending (flexure) , simple 48Ellipse 42EN 10 204 classes, material traceability
301
Engine, diesel 255brake test, diesel 257guarantee, diesel 256performance, diesel 255
Epicyclic gear sets 104Equations:
motion 65Navier–Stokes 142
ESRs 316Essential health and safety requirements
316European Commission 328
Failure mode analysis (FMA) 287, 289Fan running testing procedures 272Fin-fan cooler 270, 274Flexible couplings:
membrane-type 93, 96simple disc-type 93
Flexure 48Flow 11
axisymmetric 151compressible one-dimensional 147compressor characteristics, axial 235equations 137isentropic 146measurement, turbocompressor 199regimes 142, 144one-dimensional 137, 138two-dimensional 139, 140, 141
Flowrate, compressor 181Fluid:
couplings 123principles 139statics 137
Force 4dynamic 69
Forced vibration with damping 73Free damped vibration 72Free vibration 72Friction:
clutch 127coefficients 89
Gas, perfect 135Gas turbine:
aeroderivatives 223industrial 234inspections and testing 240propulsion terminology 223
Gears 99
Index 339
coupling 94double helical 103forces, formulae for 111inspection standards 249materials 108nomenclature 108selection 107sets, epicyclic 104spur 101train contact checks 251
Gearbox:and testing 249no-load running test 253running test – monitoring 254
General tolerances 280Gland steam system 207Greek alphabet 1GT:
air intake system 238bearings 240
sensors 242clearance checks 246industrial 238noise:
characteristics 247tests 248
no-load run test 247rotor runout measurement 243sequential combustion arrangement
238shaft bearings 241
Harmonic motion, simple 67Harmonized standards 315, 321Health and safety requirements,
essential 316Heat 8, 10Helical gears, double 103Helix 44, 45Holes 281Hyperbola 43
Improving design reliability 289Industrial GT 238Inspections and testing, gas turbine 240Isentropic flow 146ISO 1940 75
Keyed couplings 57Kinematic viscosity 17
Kinetics 102
Labyrinth gland 110Limits and fits 283
common combinations 285
Machine:elements 84vibration 75
Machinery Directive 32198/37/EC 303, 328annexes 308exclusions from 304
Machinery instruction 313Machinery noise 79Material traceability 299
EN10 204 classes 301Mechanical design, propeller 266Mechanical power transmission 90Mechanical seals 110, 114, 115Membrane-type flexible couplings 93Moment of area, second 49Motion:
angular 66equations 65
National standards 320Navier–Stokes equations 142Net Positive Suction Head (NPSH)
158, 159test 166
New approach directives 303Noise levels, typical 80Noise, machinery 79Normal shock waves 148Numbers, preferred 277
One-dimensional flow 137, 138compressible 147
Parabola 41Perfect gas 135Performance:
compressor 181guarantees, turbocompressors 197pump 158test, turbocompressor 198, 199
Plain carbon steels 295Poisson’s ratio 48
Engineers’ Guide to Rotating Equipment340
Power 11transmission, mechanical 90
Preferred numbers 277Preferred sizes 277Pressure 5, 7
conversions 6Propeller:
coefficients 265mechanical design 266
Propfans 228Proposed ‘amending’ directive
95/16/EC 326PTC-10, turbocompressors 194Pulley:
differential 130mechanisms 128
Pulsejet 223, 229Pump:
assembly checks 177balancing 172centrifugal 153
technical standards 178characteristics 162components – clearances and fits
176impeller balancing 174performance 158rotor balancing 175specific speed ns 169
Ramjet 223, 228Reliability:
assessment 288in design 287
Reynolds number 142Risk analysis 287Rocket motor 223Roller bearings 88Rotor dynamic balancing 244Rotor overspeed test 244Rotor tests 214
Screw:fasteners 83threads 282
Seals 110bellows 110mechanical 110, 114, 115
Shaft:couplings 91vibration 196
SI system 2Simple disc-type flexible couplings 93Simple harmonic motion cam 120Sine wave 44Sinks 142, 143Sizes, preferred 277Slope of beams 51, 52Sources 142, 143Special attestation procedures 306Specific speed 171
pump 169Specifications and standards,
compressor 186Speed 13Spur gears 101Stainless steel 296Stall conditions 268Standards:
and specifications, compressor 186balancing 81bearings 131gear inspection 249harmonized 315, 321national 320noise 82technical ix
centrifugal pumps 178diesel engine 259fans 269
vibration 81Statics, fluid 137Steam turbine 203
casing hydrostatic test 213expansion measurement 211gland stream system 208hydraulic oil system 207jacking oil system 206labyrinth seals 209LO system 204supervision system 210vibration monitoring 211
Steels:alloy 295, 296plain carbon 295stainless 296, 297
Strain:energy 56simple 47
Stress 11concentration factors 61simple 47
Index 341
Surface finish 286
Technical file 310Technical standards ix
centrifugal pumps 178compressor 186diesel engine 259fans 269turbines 217
Temperature 8conversion 9
Test:circuit, compressor 184diesel engine brake 257dynamic balancing 250gearbox:
no-load running 253running – monitoring 254
GT no-load run 247rotor overspeed 244steam turbine casing hydrostatic 213turbine hydrostatic 212
Testing:and gearboxes 249and inspections, gas turbine 240compressor acceptance 183GT noise 248procedures, fan running 272rotor 214turbocompressor vibration 200
Tolerances 278, 280screw threads 282
Tooth geometry 102Torque 11, 57Torsion 51, 53, 57
and bending, combined 60Turbine:
casing hydrostatic test, steam 213clearances 216drains system 209gas:
aeroderivatives 223industrial 234
gland stream system, steam 208hydraulic oil system, steam 207hydrostatic test 212jacking oil system, steam 206labyrinth seals, steam 209LO system, steam 204propulsion terminology, gas 223
steam 203expansion measurement 211
supervision system, steam 210technical standards 217vibration monitoring, steam 211
Turbochargers 260Turbocompressors 188, 191
ASME PTC-10 194vibration tests 201flow measurement 199performance:
test 198, 199guarantees 197
Turbofan 226, 227fan-jet 224
Turbojet 223, 224, 226aero 225simple 223
Turboprop 223, 224, 228Turboshaft 224, 228Two-dimensional flow 139, 140, 141
Uniform acceleration cam 120Units systems 2USCS system 2
V belts 124Vacuum breaker 207VDI 2045 193VDI 2056 249Vector algebra 27Vibration 71
bearing house 75forced with damping 73formulae 72free 72
damped 72machine 75shaft 196tests, turbocompressor 201
Viscosity 16dynamic 16kinematic 17
Waves, normal shock 148Wedge belts 124Weight 4Wheel 100Work 8Worm 100
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